Gotowa bibliografia na temat „Relativitatea generală”

În timp, teoria generală a relativității a acumulat mai multe anomalii și discrepanțe, indicând necesitatea unor teorii mai bune despre gravitație sau alte moduri de abordare. Ipotezele ad-hoc introduse în relativitatea generală pentru a explica singularitățile gravitaționale pe baza condițiilor energetice nu sunt foarte eficiente. Sunt necesare ipoteze mai detaliate asupra conținutului materiei. Mulți oameni de știință și filosofi au ajuns la concluzia că singularitățile trebuie să fie asociate cu atingerea limitelor valabilității fizice a relativității generale, fiind nevoie să se dezvolte o nouă teorie, a gravitației cuantice.

Cele mai multe experimente au confirmat relativitatea generală cu ajutorul tehnologiilor nou dezvoltate. S-a creat o bază tehnologică pentru astronomia undelor gravitaționale. S-au construit antene barogene criogenice și antene interferometrice laser performante, asociate cu analiza teoretică a experimentelor cu masele de testare, rezultând că sensibilitatea experimentelor depinde de izolarea termică, dacă dispozitivul înregistrează continuu coordonatele sensibilitatea antenei este limitată, și se poate crește sensibilitatea dacă se folosesc proceduri cuantice. Antenele pot ajuta în observarea radiației gravitaționale de fond și testarea relativității generale în cazul ultra-neliniar.

Extreme-Mass-Ratio Inspirals (EMRIs) són sistemes binaris que estan compostos per Objectes Estel.lars Compactes (OECs) orbitant al voltant de Forats Negres Massius (FNMs) situats als centres galàctics. Aquests sistemes són una de les fonts pricipals d’Ones Gravitacionals (OGs) per detectors espacials com l’antena espacial LISA (Laser Interferometer Space Antenna). Un EMRI emet senyals molt llargs i complexes dintre del fort camp gravitatori del FNM. Aquests senyals porten codificada l’estructura del FNM. Per aquest motiu, les OGs procedent d’EMRIs són una font valuosa per estudiar els FNMs situats als centres galàctics i la ciencia relacionada amb ells. En aquesta tesi estudiem dos aspectes diferents dels EMRIs: El seu modelatge i l’estimació dels paràmetres del sistema a partir dels seus senyals gravitatoris. La primera part d’aquesta tesi està dedicada al modelatge d’EMRIs, necessari per obtenir les formes d’ona de les OGs que farem servir en la seva detecció. Per aquest motiu, necessitem conèixer com el camp gravitatori del OEC afecta la seva propia trajectoria i el desvia d’un moviment geodèsic. En aquest sentit, degut a la gran diferència entre les masses del sistema, podem considerar l’OEC com a una partícula sense estructura que orbita en una geodèsica del FNM. En aquesta representació, la caiguda en espiral del OSC al voltant del FNM ve descrita per l’acció d’una autoforça local, la qual altera el moviment geodèsic de la partícula. No obstant, la implementació d’aquest mecanisme presenta diverses dificultats, degut principalment a que la descripció de l’OEC com un punt introdueix distribucions del tipus delta de Dirac. Aixó a la pràctica significa que hem de tractar amb escales temporals i espacials molt diferents, les quals estan associades al modelatge del FNM i al modelatge de l’OEC. En aquesta tesi presentem un mètode novel, el qual anomenem l’esquema de la Particle-without-Particle (PwP), que proporciona cálculs molt precisos i eficients de l’autoforça en el domini temporal, el que fa de la nostra tècnica adequada pels càlculs intensius que es requereixen en els escenaris astrofísics relevants. El punt clau del nostre métode és que no resolvem l’OEC. En el seu lloc, evitem incloure la seva presència en el (multi-)domini computacional, sustituint la delta de Dirac per condicions de contorn. Conseqüentment, només hem de proporcionar la resolució numèrica necessaria per descriure el camp aprop l’OSC, però no l’OSC mateix. D’aquesta manera tots el problemes relacionats amb la resolució d’una escala petita desapareixen. El treball desenvolupat en aquesta tesi, pot ser millorat in termes de temps de computació i putser en precisió si explorem diferent tècniques per portar el els contorns exteriors del domini computacional més aprop de la parícula sense degradar la precissió dels valors del camp a prop d’ella. Aixó es podria fer millorant les condicions de contorn exteriors o compactificant el domini físic. Hi han dos possibilitats més que podem explorar per fer els nostres càlculs més rápids, que són: (i) Reduïr el pas temporal de les nostres evolucions numèriques i (ii) paral.lelitzar el nostre codi i fer servir ordinadors amb múltiples cors (encara que aixó no incrementaria el temps de CPU). Degut a que en le cas d’un FNM de tipus Schwarzschild, com el presentat en aquesta tesi, els diferents modes no estan acoplats, en pricipi això no hauria de ser una tasca difícil d’assolir. A més a més, podem fer servir extrapol.lacions Richardson per millorar l’estimació dels valosrs de l’autoforça. Aquestes millores es poden aplicar perfectament dintre del nostre marc computacional i ténen un potencial significatiu per milloar l’eficiència dels nostres càlculs. Finalment, l’objectiu principal de la formulació presentada en aquesta tesi és desenvolupar un mètod acurat i eficient per calcular l’autoforça en situacions d’interés físic. En particular, per sistemes d’interés pel futur observatory espacial LISA. Aixó significa extendre aquestes tècniques pel cas gravitatori i per FNs amb rotació. En aquest sentit, hem de fer menció que encara que transferir les nostres técniques al cas gravitatori és directe, fer el mateix pel cas d’un FN en rotiació requereix noves millores que seran l’objectiu d’investigacions futures. En la segona part de la tesi, investiguem si és o no possible fer servir observacions d’EMRIs per testejar una determinada teoria de la Gravetat, en particular la teoria Dinàmica Chern- Simons de la Gravetat Modificada (DCSGM). La idea és que l’OEC orbita en la part més profunda del potencial gravitatori del FNM, això és els sistemes EMRI emeten OGs desde la regió de camp gravitatori fort del FNM. D’aquesta manera, la forma i el ritme de les OGs emesses pel sistema porten codificades l’estructura de l’espaitemps del FNM i la forma en la que les freqüències característiques del sistema evolucionen. Aquesta informació és la que ens permet realitzar tests de la RG. Amb aquesta finalitat, hem obtingut les forma d’ona emesses per l’OEC en una geometria del FNM que ha sigut modificada amb correccions Chern-Simons (CS). L’estimació dels paràmetres del sistema s’ha dut a terme fent servir anàlisis de Fisher matrix. Hem començat estudiant un sistema típic EMRI en RG i hem trobat que els nostres resultats coincidien amb resultats previs que es troven en la literatura. Seguidament, hem realitzat estudis d’estimacions de paràmetres per determinar l’habilitat de LISA per distingir entre RG i DCSGM, en particular per estimar el paràmetre de CS , el qual diferencia les mètriques de la DCSMG i de la RG. Amb aquesta finalitat, hem realitzat simulacions d’un sistema EMRI que cau en el punt de la banda de LISA amb sensibilitat màxima i que hem fet evolucionar durant els sis mesos abans de la col.lisió de l’OSC amb el FNM. Els nostres reultats indiquen que per determinats sistems EMRI, un detector com LISA podría discriminar entre RG i DCSGM. També hem vist que l’error en estimar disminueix amb la massa del FNM. Per tal de millorar els nostres reusltats, voldriem realitzar un estudi més exhaustiu de l’espai de paràmetres dels EMRIs. En un futur voldriem estudiar tòpics com ara comparar o esimar els errors que poden sorgir fent servir formes d’ones de RG per detectar EMRIs en DCSGM. A tal efecte, hem d’estimar la magnitud de l’error del nostre model. Ens agradaria extrendre l’estudi presentat en aquesta tesis per altres detectors d’OGs com, per exemple, Intermediate-Mass-Ratio Inspirals (IMRIs) en l’Einstein Telescope.
Extreme-Mass-Ratio Inspirals (EMRIs) are binary systems which are made up of a Stellarmass Compact Object (SCO) orbiting around a Massive Black Hole (MBH) located in a galactic centre. These systems are one of the main sources of GWs for space-based detectors like the Laser Interferometer Space Antenna (LISA). EMRIs emit long and complex GWs signals in the strong field regime of the MBHs, which encode the MBH structure. For this reason, EMRI GW signals are a valuable tool to study the MBHs located in the galactic centres and the science related with them. In this thesis, we study two different aspects of EMRIs, namely modelling and the parameter estimation of the system from their gravitational signals. The first part of the thesis is devoted to the modelling of EMRIs, to produce the GW waveforms needed for their detections. To that end, we have to know how the gravitational field of the SCO affects its own trajectory and deviates it from geodesic motion. In this regard, due to the extreme mass-ratio of the system, we can consider the SCO as a structureless particle orbiting in a geodesic of the exact MBH geometry. In this picture, the inspiral of the SCO around the MBH is described through the action of a local self-force, which alters the geodesic motion of the particle. However, the implementation of this mechanism presents several difficulties, mainly due to the point-like description of the SCO, which introduces Dirac delta distributions. This in practice means that one has to deal with very different spatial scales, one associated with the modelling of the SCO and another associated with the MBH. Moreover, the extreme mass ratio of these systems implies that we have to deal with two different time scales in the dynamics of the system, one associated with the orbital evolution of the SCO and another associated with the evolution of its orbit due to GW emission. We present a new method, which we call the Particle-without-Particle (PwP) method, that provides very efficient and accurate computations of the self-force in the time-domain, which makes our technique amenable for the intensive computations required in the astrophysically relevant scenarios. The key point of our scheme is that it does not need to resolve the SCO. Instead, we avoid its presence in the computational (multi-)domain by substituting the Dirac delta distributions by boundary conditions. Consequently, we have just to provide the numerical resolution to describe the field near the SCO, but not the SCO itself. In this way, the equations that we have to solve inside each subdomain are homogeneous wave-type equations for the fields. Consequently, all the problems related with the numerical resolution of a small scale disappear. The work we have presented here can be further improved in terms of computational time, and perhaps in accuracy, by exploring techniques to bring the outer boundaries closer to the particle without degrading the accuracy of the field values near it. This can be done either by improving the outgoing boundary conditions or by compactifying the physical domain. There are two more possibilities for making our computations faster, which are: (i) To reduce the time step of our numerical evolutions and, (ii) to parallelise our numerical code and use computers with many cores (although this does not decrease the CPU time). Since for a Schwarzschild MBH case, like the ones studied in this thesis, the different modes are not coupled, this is in principle a simple task. In addition, we can introduce Richardson extrapolation, to improve the estimations of the values of the self-force. These improvements can be perfectly applied to our framework and have significant potential to improve the efficiency of the computations. Since, the main goal of the formulation presented in this thesis is to develop an accurate and efficient method to compute the self-force in situations of physical interest. In particular, for systems of interest for the future observatory LISA. This means to extend these techniques for the gravitational case and for spinning MBHs. In this sense, we have to mention that while it is straightforward to transfer these techniques discussed here to the gravitational case, to do the same with the case of a spinning black hole may require new technical improvements which we will the subject of future investigations. In the second part of the thesis, we investigate whether we can use EMRI observations to test a particular theory of Gravity, namely Dynamical Chern-Simons Modified Gravity (DCSMG) theory. The idea is that the SCO orbits are deep inside the MBH gravitational potential, that is, EMRI systems emit GWs from the strong field region of the MBH. In this way, the shape and timing of the GWs emitted by the system have encoded the structure of the MBH spacetime and the way in which the characteristic frequencies of the system evolve. This information allows us to perform tests of GR and even of other theories of gravity, in particular, we have focused on the possibility of distinguishing between GR and Dynamical Chern Simons Modified Gravity (DCSMG). To that end, we have computed the waveforms emitted by an SCO orbiting in a MBH geometry which have been modified with CS corrections. The parameter estimation has been performed employing Fisher matrix analysis. First of all, we have studied a typical EMRI system in GR and we have found agreement between our results and previous ones found in the literature. Afterwards, we have performed parameter estimation studies to estimate the ability of LISA to distinguish between GR and DCSMG, in particular by estimating the CS parameter , which differentiates the DCSNG metric from the GR one. To that end, we have performed simulations of an EMRI system which falls in the sweet spot of the LISA sensitivity band and which has been evolved during the last six months before plunge. Our results indicates that for certain EMRI systems a detector like LISA may discriminate between GR and DCSMG. We have also seen that the error in estimating decreases with the MBH mass. In order to improve the present results, we would like to perform a more exhaustive study of the parameter space of EMRIs. In the future, we would like to address topics like to compare or estimate the errors that could arise using GR waveform templates to detect EMRIS in DCSMG. To that end, we should estimate the magnitude of the model errors. We would like to extend the study presented in this thesis to other GW detectors like, for instance, Intermediate-Mass-Ratio Inspirals (IMRIs) in the Einstein Telescope.

En el presente trabajo analizo desde un punto de vista crítico el episodio que representa “Gravity Probe B” (GPB) (La Sonda de la Gravedad B) en la historia de la experimentación en la física fundamental. Anunciado como una “Prueba del Universo de Einstein”, GPB fue un experimento para examinar predicciones de la teoría general de la relatividad (TGR) que duró 50 años. GPB nació en Stanford University, en el momento que el principio de la tecnología de satélites lo convirtió en una posibilidad y se convirtió en el proyecto más longevo de la NASA: los resultados finales se publicaron en el año 2011. Siguiendo el diseño original de 1960, GPB pretendió medir el arrastramiento del marco espaciotemporal y el efecto geodésico sobre un giroscopio en órbita alrededor de la tierra en un satélite funcionando en modo “drag-free” (sin resistencia). Siguiendo una órbita puramente gravitacional, junto con el giroscopio y los magnetómetros formados por dispositivos superconductores de interferencia cuántica, la nave espacial contenía un telescopio que rastreaba una estrella guía como punto de referencia. La misión espacial empezó en el 2004 y concluyó en el 2005 con el objetivo de medir el cambio en la orientación del eje de giro de los giroscopios, relativo al inmóvil espacio inercial, con una precisión de 0.5 milésimas de un segundo de arco ($sim 10^{-7}$ grados) a lo largo de un año. Para realizar el experimento fue necesario desarrollar varias tecnologías completamente novedosas, y los sistemas de abordo diseñados establecieron varios récords por ser los sistemas más cerca de la perfección diseñados jamás. (GPB) representa una oportunidad única para analizar cómo funcionan los experimentos científicos extremos y una gran oportunidad de estudiar los esfuerzos para generar conocimiento acerca de la TRG basado en la experimentación. GPB se encontró con serias dificultades durante la ejecución, con importantes anomalías y un ruido excesivo en los datos. El equipo se vio obligado a desarrollar controvertidos métodos nuevos para analizar los datos que se obtuvieron. Inicialmente presento tanto la física relevante a la aproximación específica a la TRG apropiada para analizar la gravitación en el sistema solar (el marco posnewtoniano de parametrización) como la historia de la confirmación de TRG. Después de presentar GPB y sus objetivos, introduzco el marco analítico que adopto para examinar los resultados y conclusiones que el equipo logró. Utilizo el trabajo de James Woodward y Deborah Mayo, combinándolo en una perspectiva basada en tres puntos: los datos observados pueden ser evidencia para fenómenos teóricos subyacentes; la experimentación hace lo posible para rastrear la veracidad de las hipótesis a través de la sensibilidad contrafáctica de los datos a las afirmaciones teóricas; y para que los datos valgan como evidencia a favor de un fenómeno, la prueba que represente el encaje de estos con las predicciones de las hipótesis examinadas debe ser severo, aunque no necesariamente represente un uso novedoso de los datos. Destaco muchas preocupaciones con el análisis de los datos producidos por GPB, pero a través de mi análisis basada en este marco, mi conclusión es que las afirmaciones del equipo de GPB son perfectamente válidas. También indico que este episodio demuestra que puede ser importante que los científicos adopten las perspectivas más sofisticadas propuestas por filósofos en lugar de contar con los más comunes acercamientos epistemológicos. Finalmente, indico que a pesar de la posibilidad de que el conocimiento generado no sea del todo sólido e inmóvil, y que algún día pueda revisarse, cumple con los requisitos más estrictos que la sociedad normalmente pide de las conclusiones de la investigación.
In this thesis, I critically analyse Gravity Probe B (GPB) as an extraordinary episode in the history of experimentation in fundamental physics. Billed as “Testing Einstein’s Universe,” GPB was a 50-year-long experiment to test crucial predictions of the General Theory of Relativity (GTR). GPB started life at Stanford University when satellite technology first made the “Relativity Gyroscope Experiment” feasible and it went on to become the longest running mission in NASA’s history; final results were published in 2011. Following the original design published in 1960, GPB set out to measure frame dragging (also known as the Lense-Thirring effect) and the geodetic (or de Sitter) effect on a superconducting gyroscope orbiting the Earth in a “drag-free” satellite. Essentially executing a purely gravitational orbit, together with the science instrument assembly containing the (multiple) gyroscope(s) and superconducting quantum interference devices used as magnetometers, the spacecraft housed a telescope trained on a reference “guide star”. The mission flew from 2004 to 2005 and aimed to measure the change in the orientation of the spin axis of the gyroscopes, relative to “fixed” inertial space identified using the guide star, to within 0.5 milliarcseconds (~10-7 degrees) over the year-long experiment. The experiment required the development of several completely new technologies before it could be performed and the on-board systems broke numerous records as the most nearly perfect and most sensitive systems created. It represents a unique opportunity to analyse the workings of scientific experimentation taken to the extreme and a rare chance to examine efforts to generate knowledge based on experimental GTR: one of our two current fundamental physics theories. GPB encountered serious problems during execution of the space mission with major anomalies and excessive noise in the data collected. The team was forced to develop controversial new data analysis methods to attempt to salvage meaningful results from the unexpected and unrepeatable dataset they retrieved. I initially present both the physics of GTR in the specific weak gravity approximation appropriate for analysing gravitational effects within the Solar System (the parametrised post-Newtonian framework) and the prior history of confirmation of GTR. After presenting GPB and its aims, I then introduce the analytical framework that I adopt to examine the claims made by the team regarding their data analysis and eventual findings. I draw heavily on work by James Woodward and Deborah Mayo, among others, and combine this into a 3-point approach: observed data can act as evidence for underlying theoretical phenomena; experimentation contrives to track the truth of hypotheses via the counterfactual sensitivity of the data produced by the specific experimental set-up to those theoretical claims; and for data to count as evidence in favour of a phenomenon, the test that the match between them and the predictions of the hypothesis being examined represents must be severe, although not necessarily entail novel use of the data. I highlight many worries with the GPB data analysis, but through analysing it within this framework, I conclude that the claims of the GPB team are valid. I also indicate that the episode shows how it can be important for working scientists to adopt the more sophisticated approaches advocated by some philosophers rather than relying on more typical epistemological attitudes found in 20th century textbooks. I close by noting that although the knowledge gained may not be unshakeably solid and is open to future revision, it fulfils the strictest demands normally placed by society on the conclusions of investigation.

Las ondas gravitatorias primordiales representan una ventana privilegiada para determinar la evolución del Universo, ya que a partir de su espectro seria posible reconstruir el factor de escala desde los instantes iniciales de expansión hasta el instante presente. En esta tesis, trabajando en aproximación de vacío adiabático, hemos revisado como la expansión del Universo amplifica las fluctuaciones del vacío cuántico. Hemos evaluado el espectro en un modelo de expansión del universo que considera una era inicial inflacionaria, una era dominada por agujeros negros primordiales y radiación, una era dominada por radiación y finalmente una era de la materia. Hemos demostrado como el espectro de este escenario es mucho menor que el del modelo habitual (inflación- era de radiación-era de materia), también hemos visto como las anisotropías observadas del CMB ponen limites a los parámetros libres del modelo de las cuatro eras. Hemos calculado el espectro en un modelo con un universo dominado por energía oscura en la era presente, concluyendo que pese a que este espectro coincide con el del escenario de las tres eras evoluciona de manera diferente. También hemos calculado el espectro en una hipotética segunda era de la materia, en el caso de que esta era de expansión acelerada sea sólo una etapa transitoria. Hemos estudiado como se cumple la segunda ley de la termodinámica durante la era de expansión acelerada, asignando una entropía a las ondas gravitatorias primordiales que debe cumplir una determinada condición. Finalmente, dejando de lado las ondas gravitatorias, hemos estudiado la segunda ley de la termodinámica en universos dominados por energía oscura fantasma, concluyendo que la entropía de estos fluidos es negativa y que la segunda ley es respetada.
Cosmology has for a long time been a rather speculative science. Hubble's discovery that the Universe is expanding, and -more recently- the realization that at present this expansion is accelerated, the measured abundance of light elements, the mass distribution of galaxies and clusters thereof, and the discovery and posterior measurements of the anisotropies of the CMB have changed this picture. Hopefully, measurements of GWs will soon be added to this short list. At any rate, now we can speak confidently of physical cosmology as a fully-fledged branch of Science. The relic GWs constitute a privileged window to determine the evolution of the Universe. Little is known from the early evolution of the Universe and the predictions for their spectrum depend on the model considered. According to these predictions, a spectrum of relic GWs is generated making feasible its detection with the technology currently being developed. In this thesis, using the adiabatic vacuum approximation, we have reviewed how the expansion of the Universe amplifies the quantum vacuum fluctuations, and how the relic GWs spectrum is related with the scale factor. We have later evaluated the spectrum in a four-stage model (which consist on a De Sitter stage, a stage dominated by a mixture of MBHs and radiation, a radiation dominated stage and finally a non-relativistic matter (dust) dominated stage). We have demonstrated that the spectrum in this scenario is much lower than the predicted by three-stage model (De Sitter-radiation era-dust era). We have also shown how the bound over the GWs spectrum from the measured CMB anisotropies places severe constraints over the free parameters of the four-stage model. We have also considered a scenario featuring an accelerated expanding era dominated by dark energy, right after the dust era of the three-stage model. We have found that the current power spectrum of this four-stage scenario exactly coincides with that of the three-stage, but it evolves in a different fashion. We have considered as well the possibility that the dark energy decays in non-relativistic matter leading to a second dust era in the far future and obtained the power spectrum of the GWs as well as the evolution of the density parameter. We have applied the generalized second law of thermodynamics to the four-stage model of above. Assuming the GWs entropy proportional to the number of GWs, we have found the GSL is fulfilled provided a certain proportionality constant does not exceed a given upper bound. Finally, we have extended the GSL study to a single stage universe model dominated by dark energy (either phantom or not), and found that the GSL is satisfied and that the entropy of the phantom fluid is negative. Likewise, we have found a transformation between phantom and non-phantom scenarios preserving the Einstein field equations that entails a "quasi" duality between the thermodynamics of both scenarios.

In this thesis we present a new aspect pertaining to the effective field theory of general relativity in the limit of a large number D of dimensions. We demonstrate that the theory initially developed to capture the physics of asymptotically flat branes also contains a new family of localized solutions that can be identified with higher dimensional black holes such as the Schwarzschild-Thangerlini or the Myers-Perry black holes in the limit of a large number of spacetime dimensions. Using this technique we have explored several new aspects of these black hole solutions. We show that the effective large D equations for the asymptotically flat brane also contain an analytic solution that is a gaussian blob (with the same topology as the flat membrane). The blob actually corresponds to a magnification of the geometry near the cap (north-pole) of the black hole. We calculate their (slow) quasi-normal spectrum, which captures the stability of Schwarzschild black holes and also the instability of ultraspinning Myers-Perry black holes. Additionally we find novel class of rotating black bar solutions, that appear as stationary objects in the effective theory since they can not radiate gravitational waves which are decoupled from the effective theory. We describe a method that allows to construct (Maxwell) charged solutions form every non- charged solution that the large D theory contains. Using this method we construct charged and rotating black holes in the Einstein-Maxwell theory. Furthermore we explore the solutions that branch of from the (ultra-spinning) Myers-Perry (MP) black hole and the non-linear extensions of the zero-modes of the analytically known black bar. We study the evolution of higher dimensional black hole collisions by solving numerically the effective equations of motion. We demonstrate that in these collisions it is possible to form black holes with elongated horizons such as black bars and dumbbells. At high enough angular momentum the black bars and dumbbells can be so elongated that they are susceptible to a Greggory-Laflamme type instability, that leads to the a pinch off of the horizon towards a naked singularity. Accordingly this demonstrates a novel example of a violation of weak cosmic censorship in the quintessential process of general relativity: the collision of black holes. Furthermore we study the evolution and decay of ultraspinning MP black holes, and observe remarkably rich structure in the intermediate states of the decay. Lastly, we study how entropy production and irreversibility appear in the large D effective theory. With this tool we study how black hole entropy is generated in several highly dynamical processes, such as the fusion of black holes and the fission of unstable solutions into multiple black holes. We find the black hole fusion is highly irreversible, while fission which follows the decay of unstable black strings generates much less entropy. Additionally we describe how in processes that contain fusion and fission the intermediate state is quasi-thermalized.
En esta tesis hemos presentado un nuevo aspecto perteneciente a la teoría efectiva de la relatividad general en el límite de un gran número de dimensiones. Hemos demostrado que la teoría desarrollada inicialmente para capturar la física de las branas asintóticamente planas también contiene una nueva familia de soluciones localizadas que pueden ser identificadas con agujeros negros de dimensiones más altas como los agujeros negros de Schwarzschild- Thangerlini o de Myers-Perry en el límite de gran D. Usando esta técnica hemos explorado varios aspectos nuevos de dichos agujeros negros. Encontramos una nueva clase de soluciones de barras negras giratorias, que aparecen como objetos estacionarios en la teoría efectiva Describimos un método que permite construir soluciones cargadas a partir de cada solución no cargada. Usando este método construimos agujeros negros cargados y giratorios en la teoría de Einstein-Maxwell. Estudiamos la evolución de las colisiones de agujeros negros en dimensiones superiores usando las ecuaciones efectivas. Demostramos que en estas colisiones es posible formar agujeros negros con horizontes alargados como barras negras o con forma de mancuernas. Con un momento angular lo suficientemente alto, las barras negras pueden ser tan alargadas que son susceptibles a una inestabilidad tipo Greggory-Laflamme, que lleva a una rotura del horizonte y a una singularidad desnuda. Por consiguiente, esto demuestra un ejemplo novedoso de una violación de la hipótesis de 'cosmic censorship' (censura cósmica). Además estudiamos la evolución y el decaimiento de los agujeros negros MP ultraspinning, y observamos una estructura notablemente rica en los estados intermedios del decaimiento.

In this thesis we apply new approaches and develop new techniques to address various issues related to fundamental aspects of modern gravitational theory and black holes. We study the behavior of black branes in the large D approximation, that is, we consider a space with a very large number of dimensions. This approach allows us to obtain a set of very simple equations that capture many of the physical phenomena of gravity. This technique uses the fact that the gravitational field around a massive object decays faster the higher the dimension, so when you take the very large D limit it becomes concentrated in a very thin region of size 1/D around the horizon of the black hole. In this way, the horizon can be viewed as a membrane suspended in an essentially flat background geometry. The region where the black hole lives is, in some sense, excluded from the background space. We use the large D effective equations to investigate the phases and stability of black strings at different values of the dimension D and the compactification length L. In some cases, the Gregory-Laflamme instability of the uniform black strings can lead to stable non-uniform black strings. The transition type changes at a certain critical value of D ~ 13.5. We use 1/D corrections to estimate the value of the critical dimension, which turns out to be very accurate. Possible violations of Weak Cosmic Censorship in black hole collisions at D > 4 are also explored. The large D technique, through the effective equations, provides a powerful tool for analyzing such scenarios that would otherwise be very difficult to tackle using numerical simulations at finite D. It has recently been shown that rotating black holes can be described as Gaussian lumps on a black brane. The Strong Cosmic Censorship conjecture for highly charged Reissner-Nordström black holes has recently been called into question in asymptotically de Sitter spacetimes. To go beyond previous studies, this thesis includes the results of nearly extremal Reissner-Nordström nonlinear simulations. In order to perform the nonlinear (spherically symmetric) integrations, a new spectral code has been developed in double-null coordinates. Any continuous system that can be described as a quantum field theory will react to a change in the geometry where it is located. It will do so by changing its distribution of energy density, pressure and stresses. That is, the system is polarized, and its stress-energy tensor acquires a non-trivial quantum expectation value. In this context, the holographic duality, also known as AdS/CFT correspondence, is extremely useful for extracting valuable qualitative information from the system. Perturbations of the geometry of the AdS boundary will produce tidal deformations in the geometry of the bulk. To calculate this deformations, we solve the equations for a linearized perturbation of the geometry that satisfies suitable boundary conditions. Finally, we study a subset of Horndeski's theories whose equations of motion are locally well posed. However, it is necessary to determine whether global solutions exist and whether they are sufficiently well behaved. A worrisome possibility (which has been confirmed by numerical simulations) is a change in the character of the equation of motion, from hyperbolic to parabolic and finally to elliptical. This causes a change in the causal structure of the geometry.
En aquesta tesi aplicarem nous enfocaments i desenvoluparem noves tècniques per tractar diversos temes relacionats amb aspectes fonamentals de la teoria gravitacional moderna i els forats negres. Estudiem el comportament de les branes negres en l’aproximació large D, és a dir, considerem un espaitemps amb un nombre molt gran de dimensions. Aquest enfocament ens permet obtenir un conjunt d’equacions molt simples que recullen molts dels fenòmens físics de la gravetat. En alguns casos, la inestabilitat de Gregory-Laflamme de les cordes negres uniformes pot conduir a cordes negres no uniformes estables. S’exploren també possibles esdeveniments de violació de la Censura Còsmica Feble en col·lisions de forats negres a D > 4. La tècnica de large D, mitjançant les equacions efectives, proporciona una eina potent per analitzar aquest tipus d’escenaris que d’altra manera serien molt complicats d’abordar mitjançant simulacions numèriques a D finita. Recentment s’ha posat en dubte la conjectura de Censura Còsmica Forta per a forats negres de Reissner-Nordström altament carregats en espaitemps asimptòticament de Sitter. Per anar més enllà dels estudis anteriors, en aquesta tesi s’inclouen els resultats de simulacions completament no lineals de Reissner-Nordström altament carregats. Qualsevol sistema continu que es pugui descriure com una teoria quàntica de camps reaccionarà davant un canvi en la geometria on està situat. En aquest context, la correspondència AdS/CFT és extremadament útil per extreure informació qualitativa i valuosa del sistema. Les pertorbacions en la geometria de la frontera d’AdS produiran deformacions de marea en la geometria de l’interior. Per calcular aquesta deformació, resolem les equacions per a una pertorbació linealitzada de la geometria que satisfà una condició de contorn adequada a l’infinit. Finalment, s’estudia un subconjunt de les teories de Horndeski les equacions del moviment de les quals són localment ben plantejades. Tot i això, cal determinar si existeixen solucions globals i si aquestes solucions són prou ben comportades. Una possibilitat preocupant (que s’ha confirmat amb simulacions numèriques), és un canvi del caràcter de l’equació de moviment, d’hiperbòlica a parabòlica i finalment a el·líptica.

The gauge/gravity duality has proven to be a very useful tool in the understanding of quantum field theories outside the perturbative regime. In particular, holography has been able to shed light not only on generic mechanisms of strongly coupled theories, but also on processes occurred in experimental set-ups, such as the heavy ion collisions. Experimental observations such as small viscosities or fast hydrodynamization find a natural explanation when the problem is expressed in terms of gravity and black holes. Despite the successes, however, it is important to bear in mind that holography provides computational tools for toy models rather than for QCD itself, and that these models are usable only under certain assumptions. Nature is very often far more nuanced than the models physicists use to describe it. In the case of heavy ion experiments and QCD there are many features that are commonly coarse grained in the holographic computations. For instance, non-trivial RG flows or baryon currents have not been included in the holographic models until very recently, although these are very relevant to experiments, and fundamental in critical phenomena. In this thesis we present a series of works in the topics field theory and heavy ion collisions that use applied holography and numeric GR as computational tools. The unifying factor among them is that they consider gravitational set-ups beyond pure gravity to describe the physics of conserved currents, non-trivial RG flows and phase transitions. In chapter 2 we use an Einstein-Maxwell set-up to compute the collision of two shock-waves with a conserved current and the hydrodynamization of the subsequent plasma. This conserved current is used to model the baryonic charge deposition by rapidity, observed in the experiments. The simulations are done with and without including the backreaction of the Maxwell field into the metric, which corresponds to the quenched approximation for the effects of the baryon charge on the gluons. In chapter 3 we present a one parameter family of non-conformal models. By adding an scalar field with a polynomial potential to the pure gravity set-up, we can achieve a non-trivial RG flow between two fixed points in the dual field theory. In this work we compute the thermodynamics and the quasi-normal modes spectra for the homogeneous states, being the latter one of the main results of the chapter. In chapter 4 we present the first holographic shock-wave collisions in a non-conformal model. To do so, we use the model introduced in chapter 3. In non-conformal models the average pressure in equilibrium is not fixed by symmetry, but by the equation of state. Out of equilibrium the average pressure might take any value, giving a new probe for the equilibration of the system. When the plasma's average pressure is well approximated by the equation of state value, we say that the system has “EoSizied”. In this chapter we show that the EoSization can indeed happen before the plasma has hydrodynamized. Finally, in chapter 5 we explore a holographic model that can contain phase transitions. This model is the same as the one presented in chapter 3, but now taking pure imaginary numbers for the controlling parameter. In an effort to understand the instabilities present in models with phase transitions, we trigger and evolve a spinoidal instability to its inhomogeneous end state. This is done by adding a small perturbation to a uniform black brane in a locally unstable branch, triggering a Gregory-Laflamme type instability in the gravity side. The most remarkable result found in the simulation is that both the evolution and the final result are well described by second order hydrodynamics.
La cromodinàmica quàntica (QCD), la teoria que descriu la força nuclear forta, és cas paradigmàtic de teoria quàntica de camps amb fases fortament acoblades. Amb l'objectiu d'entendre en profunditat la QCD i la seva dinàmica, és va iniciar a la dècada de 1970 el programa de col·lisions de ions pesants. Aquest programa experimental té com a objectiu crear, mitjançant acceleradors de partícules, fases de QCD de-confinades i estudiar-ne les seves propietats. Entre els formalismes utilitzats per a descriure sistemes fortament acoblats, com les col·lisions d'ions pesants, hi ha la dualita “gauge/string” o holografia. L'holografia és una correspondència entre dues teories -- una teoria gauge i una teoria de cordes -- que permet fer càlculs en una de les dues teories per mitjà de la seva dual. La correspondència es pot fer servir per relacionar un plasma fortament acoblat i el seu dual, forats negres en un espai asimptòticament anti-de-Sitter (AdS), on els càlculs resulten factibles. Així, per simular la col·lisió d'ions pesants s'evoluciona numèricament la col·lisió d'ones gravitatòries en AdS, i la subseqüent relaxació del seu horitzó d'esdeveniments. En aquesta tesi s'hi presenten un seguit de treballs emmarcats en el camp de l'holografia aplicada, on s'hi considera dinàmica en models més enllà de gravetat pura. En el capítol 2 es presenta la primera simulació hologràfica de col·lisions amb càrrega bariònica, un observable accessible en els experiments. Els capítols 3, 4 i 5 estan dedicats a una família de models no conformes. En el capítol 3 se n'estudia la dinàmica prop de l'equilibri per mitjà dels modes quasi-normals. En el capítol 4 s'hi estudien col·lisions hologràfiques. Finalment en el capítol 5 es genera una inestabilitat espinoidal en un model amb transició de fase i se segueix fins a un estat final inhomogeni.

In this thesis we have made progress on the study of higher dimensional gravity by focusing on the properties of black holes and branes and their dynamics. We have developed two main projects: • provide several maps between different spacetimes • determine the hydrodynamical behavior of fluids dual to some classes of black holes This work improves the current understanding of GR in spacetimes with general dimension and gives hints for holography in spacetimes different from AdS. Here we give a brief summary of the work developed underling the main results achieved. In Chapter 2, we introduce the techniques applied for studying black brane hydrodynamics. In the long-wavelength regime, black hole dynamics can be related to fluid dynamics and one can develop effective theories which capture the hydrodynamical description of such black holes. We review two of these: the fluid/gravity correspondence and the blackfold approach. We have hence learnt that black holes behave as fluids under certain circumstances. One can therefore compute the effective stress energy tensor associated to the fluid, extract the corresponding dissipative transport coefficients and possibly perform a stability analysis. In Chapter 3, we have introduced the AdS/Ricci flat correspondence, which is a relation between a class of AdS spacetimes and Einstein solutions with zero cosmological constant. Remarkably, we have developed an extension of such correspondence to spacetimes with positive cosmological constant, including scalar matter. This AdS/dS correspondence may possibly give hints to improve our understanding of holography in dS space. We have also found a new Kerr/AdS solution with hyperbolic horizon from a known Kerr/dS one through the map. The hydrodynamics of fluids using the KK dimensional reduction was studied in Chapter 4. Choosing a generic relativistic fluid, performing a boost in N internal dimensions, compactifing them and reducing on an N dimensional torus we have obtained a charged fluid with N charges. Therefore, we have investigated the variation of the transport coefficients, the shear and bulk viscosity, of the original theory and we were also able to compute the thermal conductivity. The same analysis has been applied to a particular fluid: the fluid dual to a black p-brane. We were able to compute the shear viscosity, bulk viscosity and thermal conductivity matrix for a black p-brane with N charges in the compact directions. This method is particularly interesting since it allows studying the hydrodynamics of charged objects without performing a perturbative analysis but only applying dimensional reduction techniques. Using the AdS/Ricci flat correspondence we have checked that our mapped transport coefficients coincide with the ones obtained for a known charged AdS black branes. In Chapter 5 we have investigated the hydrodynamics properties of fundamentally charged (dilatonic) black branes and branes with Maxwell charge smeared over their worldvolume. We have determined the dissipative behavior of the effective fluids associated to those branes in terms of the transport coefficients of the effective stress energy tensor. Studying the response to small long-wavelength perturbations we have analyzed the dynamical stability of both classes of charged black branes. We have moreover modified the AdS/Ricci flat correspondence to include charged cases using a non-diagonal KK reduction. In this thesis we have shown how higher dimensional gravity is surprisingly rich of new phenomena and bizarre features. Playing with spacetime dimension is the key to probe GR. Hopefully, we will able to improve our comprehension of this mysterious and powerful theory. Holography is an extremely useful tool available for this aim. Mapping apparently unrelated theories living in different number of dimensions has revealed various successful predictions and results but above all opens new perspective for our perception and understanding of GR.
Esta tesis se centra principalmente en el estudio de la gravedad en dimensiones superiores con un enfoque en las relaciones entre diferentes tipos de espaciotiempo y el análisis y caracterización de agujeros negros. Para este último objetivo hemos desarrollado y adaptado teorías efectivas que nos permiten estudiar la dinámica de agujeros negros en ciertos regímenes. Hemos presentado dos de ellas: la "fluid/gravity correspondence" y el metodo de "blackfold". Se puede demostrar entonces que los agujero negros admiten una descripción hidrodinámica y se puede calcular el tensor energía-impulso asociado al fluido dual al agujero negro y extraer los coeficientes de transporte al primer orden en derivadas. Hemos utilizado estas técnicas para analizar propiedades hidrodinámicas de branas negras en el caso en que las branas llevan cargas de diferentes tipos. En particular, consideramos los casos en que la brana negra está acoplada a un potencial de (p+1)-forma, que llamamos brana con carga fundamental, y brana acoplada a un campo de Maxwell. También hemos investigado las propiedades de estabilidad de estos sistemas hidrodinámicos . Otra línea de investigación es el estudio de la hidrodinámica de fluidos utilizando la reducción dimensional de Kaluza Klein. Empezamos considerando un fluido genérico y luego hemos particularizado el cálculo al fluido dual a una p-brana negra. Hemos investigado como varían los coeficientes de transporte de la teoría inicial como la "shear and bulk viscosity" y además hemos conseguido calcular la matriz de conductividad térmica. Como último proyecto hemos desarrollo mapas entre espaciotiempos diferentes. En particular hemos extendido el "AdS/Ricci-flat correspondence" para espacios de Einstein con curvatura positiva y negativa. Una vez derivado el mapa, lo hemos aplicado a espacios de Sitter (dS) y AdS y a agujeros negros de Schwarzschild-dS/AdS. Además, hemos estudiado perturbaciones en la frontera de AdS, que a través del mapa nos dan sugerencias sobre una posible construcción de holografía en espacio de dS. De hecho, la frontera de un espacio asintóticamente AdS se mapea en una brana en el centro de dS y las perturbaciones cerca de la frontera tienen como fuente un tensor energía-impulso confinado en esta brana.

This thesis has focused entirely on classical and thermodynamical aspects of black hole physics. We have developed four different projects involving different kinds of black holes. 1 BLACK BRANES IN A BOX Neutral black branes with extended horizons are dynamically unstable to long wavelength perturbations along their horizons; this instability is known as the Gregory-Laflamme instability. In some regimes, the dynamics of black branes can be captured by an effective hydrodynamic description. We have studied the effective hydrodynamics of neutral black branes inside a cylindrical cavity to investigate their dynamic and thermodynamic instabilities. We have used the size of the box as a control parameter for stability (smaller cavities increase rigidity and contribute to the stability of the solutions); we have ob¬served that both instabilities disappear at the same critical value of the cavity radius. We have discussed the Correlated Stability Conjecture, which relates thermodynamic and dynamic instabilities in these objects and we have argued that its correct interpretation is given by the Correlated Hydrodynamic Stability (CHS). The CHS relates the presence of unstable hydrodynamic modes to the local thermodynamic instability; this is transparent in our approach. In the effective fluid description we have computed the specific quantities that characterize the fluid. Finally we have studied the system close to the critical point at which the instability disappears and we have obtained that the wave number that marks the onset of the instability vanishes with a critical behaviour ruled by a critical exponent of 1/2. 2 BLACK STRING FLOW We have constructed an event horizon describing a heat flow, that remains constant in time, between to asymptotic regions at constant temperature. This horizon is the smooth interpolation between the horizon of a black string and a planar acceleration horizon. This was the first exact description of a flowing horizon connecting a stringlike horizon with a planar one (this can also be an infinitely big spherical black hole); the construction is valid for any number of dimensions greater than four. We obtained the horizon generators as well as the exact geometry and we showed that this horizon resembles that of flowing funnels. We computed a surface gravity that approaches on one end, the black string's surface gravity, and on the other, the infinite black hole's surface gravity which is 0. We also computed the expansion associated to the horizon generators and it vanishes in both asymptotic regions; thus reflecting the property that the black string flow horizon interpolates between two asymptotic horizons, each of which is asymptotically in equilibrium at different temperature. This construction shows that stationary black holes with non-killing horizons are possible with non-AdS asymptotics. 3 BUMPY BLACK HOLES We have constructed numerically three new families of stationary black holes with a single angular momentum. These black holes have spherical topology but they differ from the Myers Perry solution (higher dimensional generalisation of Kerr solution) in that the radius of the sphere transverse to rotation varies non-monotonically with the polar angle. We have seen that half of these solutions connect, in the space of solutions, the Myers Perry family with other families featuring non-spherical topology such as the black ring, the black saturn, etc. We found strong evidence for the presence of cones in the horizons of solutions close to the topological transition in solution space. The other half of the solutions spread widely in the rotation plane and develop a singularity along their equator. These probably do not connect to other stationary black hole branches. We have also studied stability properties of all branches. 4 BLACK HOLE MERGER We have described in an exact analytic way the event horizon of a black hole merger in the extreme mass ratio (EMR) limit; we have done it for four and five dimensions. Curiously numerical computation in which the ratio of the masses is large are difficult and not very well studied. We hope our exact result can serve as check/guide for future results in the area. We constructed the event horizon of this dynamical process by computing its null generators. We extracted a number of parameters that characterise the merger. We identified the line of caustics, the critical radius at which both horizons touch, the big horizon relaxation timescale among other things. We showed that our hypersurface describes all possible mergers, in the EMR limit, for which the small black hole is non-rotating. Finally we analysed the instants shortly before and after the pinch-on and found evidence for critical behaviour in the forming of the cusp and in the initial growth of the throat.
Esta tesis está enmarcada en el campo de los agujeros negros. En ella se han realizado cuatro proyectos que involucran diferentes tipos de agujeros negros. 1 BRANAS NEGRAS Hemos estudiado el sistema de una brana dentro de una cavidad cilíndrica con condiciones de Dirichlet para investigar la relación entre las inestabilidades dinámicas y termodinámicas presentes en la brana. Hemos empleado las técnicas de la teoría efectiva de worldvolumes para tiranas; en esta teoría la descripción del sistema (en algunas condiciones) se da a través de variables y ecuaciones hidrodinámicas. Hemos estudiado el cambio de la inestabilidad de Gregory-Laflamme al variar el radio de la caja. Hemos identificado el radio crítico que estabiliza las soluciones y el comportamiento crítico de la inestabilidad en ese punto. 2 AGUJEROS NEGROS QUE FLUYEN Hemos construido un horizonte de sucesos que describe un flujo de calor, constante en el tiempo, entre dos regiones asintóticas a temperatura constante. Este horizonte es la interpolación entre el horizonte de una cuerda negra y un horizonte planar. La cuerda negra tiene cierta temperatura y el horizonte planar, en este caso, está a temperatura cero. La construcción se ha hecho en espacio asintóticamente plano, mostrando así que una constante cosmológica negativa no es estrictamente necesaria para la existencia de agujeros negros estacionarios con que no son de Killing. 3 AGUJEROS NEGROS BUMPY Hemos construido numéricamente tres familias nuevas de agujeros negros estacionarios con un solo momento angular en seis dimensiones. Estos agujeros tienen topología esférica pero el radio de la esfera transversa a la rotación varía de manera no monótona a lo largo del ángulo polar. La mitad de estas soluciones conectan a la familia de Myers Perry con otras de topología no esférica como el anillo negro o el saturno negro, etc. La otra mitad, se extienden mucho en el plano de rotación y acaban por tener una singularidad localizada en el ecuador. 4 FUSIÓN DE AGUJEROS NEGROS Para el caso en que las masas de dos agujeros negros difieran mucho una de la otra hemos mostrado que una descripción analítica del proceso de fusión de dos agujeros negros es posible. Hemos obtenido los rayos de luz que generan el horizonte de sucesos de una colisión de agujeros negros en el límite de razón de masas extremas. Extraemos propiedades importantes y damos una caracterización muy completa del proceso de fusión.

This thesis has been devoted to the study of the gravitational collapse of spherically symmetric perturbations on a Friedman-Robertson-Walker (FRW) universe filled by a perfect fluid. Large cosmological perturbations generated by inflation, are known to be statistically almost spherical. For this reason, this thesis aims to provide the conditions for Primordial Black Hole (PBH) formation due to the collapse of inflationary density fluctuations. PBHs are considered one of the best candidate for the missing dark matter (DM). To simulate the collapse of large spherical overdensities, it has been used a pseudo-spectral method which maps differential equations into an algebraic system. The numerical code developed, allows to outline the conditions for black hole formation with a greater than ever precision in some extreme cases. By using a combination of an excision technique and analytical estimations of accretion rates, it was found that the estimation of the black hole’s masses via a self-similar scaling law, gets worse and worse for larger and larger values. In addition, it was also found that the accretion of the BH masses relevant for the DM abundance, follows the law MBH,f roughly equal to 3MBH,i where, MBH,I is the initial mass of the BH at the time of apparent horizon formation and MBH,f is the final mass of the BH after the accretion process. In the case in which the fluid permeating the universe is of the form p equal to wρ, where p is the pressure, ρ is the density of the fluid and w is a constant, it is here shown that for w greater or equal to 1/3 the conditions for black hole formation, to a very good approximation, only depend upon the curvature of the local excess-mass (compaction function) around its peak value (δc), δc (the ”threshold” for PBH formation) and the equation of state of the collapsing fluid. This fact, has been used to build an analytical formula for δc in the case of w greater or equal to 1/3, which is accurate enough to be used for cosmological applications, conversely to previous attempts. For smaller w’s instead, the knowledge of the full shape of the compaction function is necessary, in contradiction to previous claims. Moreover, while the threshold for w greater or equal to 1/3 does not strongly depend from the full shape of the compaction function, in this thesis it is also shown that the BH mass does. While inflationary fluctuations are predominantly Gaussianly distributed at the cosmic microwave back-ground scales, those leading to PBH formation at smaller scales can have larger non-Gaussianities (NG). In the final part of this thesis, it was considered the effect (numerically and analytically) of those NG to the threshold for primordial black hole formation. By monitoring the non-gaussian parameter fNL, it was found that; i) for fNL roughly greater than 3.5, the population of PBH coming from false vacuum regions dominates over that coming from the collapse of large adiabatic overdensities; ii) the effect of the statistical dispersion of profiles is small in determining δc of the mean profile.
Esta tesis pretende proporcionar las condiciones necesarias para la formación de Agujeros Negros Primordiales (PBHs) producidos por el colapso de perturbaciones cosmológicas. Los PBHs se consideran uno de los mejores candidatos para la materia oscura, cuya composición es todavía un misterio. Para simular el colapso de grandes sobredensidades esféricas y obtener las condiciones para la formación de un PBH, se ha utilizado un método pseudoespectral que mapea ecuaciones diferenciales en un sistema algebraico. En el caso en el que el fluido que impregna el universo se comporte como un fluido perfecto (p igual a wρ, donde p es la presión, ρ es la densidad del fluido y w es una constante), hemos comprobado que para w mayor o igual a 1/3 las condiciones para la formación de un agujero negro, en una muy buena aproximación, solo dependen de la curvatura del exceso de masa local (también llamado función de compactación) alrededor de su valor máximo (δc) , δc (el ” umbral ” para la formación de PBH) y la ecuación de estado del fluido que colapsa. Este remarcable resultado se ha utilizado para construir una fórmula analítica para δc en el caso de w mayor o igual a 1/3, que es lo suficientemente precisa como para usarse en aplicaciones cosmológicas. En cambio, para w más pequeños, es necesario conocer la forma completa de la función de compactación. Por otro lado, si bien es cierto que las fluctuaciones inflacionarias se distribuyen predominantemente de manera gaussiana en las escalas del fondo de microondas cósmicas, las que conducen a la formación de PBH a menores escalas pueden distribuirse de forma altamente no gaussiana (NG). En la parte final de esta tesis, se ha considerado el efecto de esas NGs en el umbral de formación de agujeros negros primordiales, tanto numérica como analíticamente.