Relevant bibliographies by topics / Higher dimensional General Relativity

Academic literature on the topic 'Higher dimensional General Relativity'

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Published: 9 March 2023
Last updated: 10 March 2023

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Journal articles on the topic "Higher dimensional General Relativity"

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Reddy, D. R. K., and R. L. Naidu. "A Higher Dimensional Inflationary Universe in General Relativity." International Journal of Theoretical Physics 47, no. 9 (February 6, 2008): 2339–43. http://dx.doi.org/10.1007/s10773-008-9667-4.

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Rahaman, F., Saibal Ray, M. Kalam, and M. Sarker. "Do Solar System Tests Permit Higher Dimensional General Relativity?" International Journal of Theoretical Physics 48, no. 11 (August 18, 2009): 3124–38. http://dx.doi.org/10.1007/s10773-009-0110-2.

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WITEK, HELVI. "NUMERICAL RELATIVITY IN HIGHER-DIMENSIONAL SPACE–TIMES." International Journal of Modern Physics A 28, no. 22n23 (September 20, 2013): 1340017. http://dx.doi.org/10.1142/s0217751x13400174.

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Black holes are among the most exciting phenomena predicted by General Relativity and play a key role in fundamental physics. Many interesting phenomena involve dynamical black hole configurations in the high curvature regime of gravity. In these lecture notes I will summarize the main numerical relativity techniques to explore highly dynamical phenomena, such as black hole collisions, in generic D-dimensional space–times. The present notes are based on my lectures given at the NR/HEP2 spring school at IST/Lisbon (Portugal) from March 11–14, 2013.
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Chiba, T. "Cylindrical Dust Collapse in General Relativity: Toward Higher Dimensional Collapse." Progress of Theoretical Physics 95, no. 2 (February 1, 1996): 321–38. http://dx.doi.org/10.1143/ptp.95.321.

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Ishibashi, Akihiro. "Symmetry Properties of Black Holes in Higher Dimensional General Relativity." Progress of Theoretical Physics Supplement 172 (2008): 202–9. http://dx.doi.org/10.1143/ptps.172.202.

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Kandalkar, S. P., and S. P. Gawande. "Anisotropic fluid distribution in higher dimensional general theory of relativity." Astrophysics and Space Science 315, no. 1-4 (April 26, 2008): 87–91. http://dx.doi.org/10.1007/s10509-008-9800-0.

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REALL, HARVEY S. "HIGHER DIMENSIONAL BLACK HOLES." International Journal of Modern Physics D 21, no. 12 (November 2012): 1230001. http://dx.doi.org/10.1142/s0218271812300017.

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MONTE, EDMUNDO M. "EMBEDDING VERSUS IMMERSION IN GENERAL RELATIVITY." International Journal of Modern Physics A 24, no. 08n09 (April 10, 2009): 1501–4. http://dx.doi.org/10.1142/s0217751x09044887.

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We briefly discuss the concepts of immersion and embedding of space-times in higher-dimensional spaces. We revisit the classical work by Kasner in which he constructs a model of immersion of the Schwarzschild exterior solution into a six-dimensional pseudo-Euclidean manifold. We show that, from a physical point of view, this model is not entirely satisfactory, since the causal structure of the immersed space-time is not preserved by the immersion.
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Aygün, M., S. Aygün, I. Yilmaz, H. Baysal, and I. Tarhan. "Møller Energy–Momentum Complex in General Relativity for Higher Dimensional Universes." Chinese Physics Letters 24, no. 7 (June 28, 2007): 1821–24. http://dx.doi.org/10.1088/0256-307x/24/7/010.

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Ashtekar, Abhay, and David Sloan. "Action and Hamiltonians in higher-dimensional general relativity: first-order framework." Classical and Quantum Gravity 25, no. 22 (November 3, 2008): 225025. http://dx.doi.org/10.1088/0264-9381/25/22/225025.

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Dissertations / Theses on the topic "Higher dimensional General Relativity"

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Durkee, Mark N. "New approaches to higher-dimensional general relativity." Thesis, University of Cambridge, 2011. https://www.repository.cam.ac.uk/handle/1810/240580.

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This thesis considers various aspects of general relativity in more than four spacetime dimensions. Firstly, I review the generalization to higher dimensions of the algebraic classification of the Weyl tensor and the Newman-Penrose formalism. In four dimensions, these techniques have proved useful for studying many aspects of general relativity, and it is hoped that their higher dimensional generalizations will prove equally useful in the future. Unfortunately, many calculations using the Newman-Penrose formalism can be unnecessarily complicated. To address this, I describe new work introducing a higher-dimensional generalization of the so-called Geroch-Held-Penrose formalism, which allows for a partially covariant reformulation of general relativity. This approach provides great simplifications for many calculations involving spacetimes which admit one or two preferred null directions. The next chapter describes the proof of an important result regarding algebraic classification in higher dimensions. The classification is based upon the existence of a particular null direction that is aligned with the Weyl tensor of the geometry in some appropriate sense. In four dimensions, it is known that a null vector field is such a multiple Weyl aligned null direction (WAND) if and only if it is tangent to a shearfree null geodesic congruence. This is not the case in higher dimensions. However, I have formulated and proved a partial generalization of the result to arbitrary dimension, namely that a spacetime admits a multiple WAND if and only if it admits a geodesic multiple WAND.Moving onto more physical applications, I describe how the formalism that we have developed can be applied to study certain aspects of the stability of extremal black holes in arbitrary dimension. The final chapter of the thesis has a rather different flavour. I give a detailed analysis of the properties of a particular solution to the Einstein equations in five dimensions: the Pomeransky-Sen'kov doubly spinning black ring. I study geodesic motion around this black ring and demonstrate the separability of the Hamilton-Jacobi equation for null, zero energy geodesics. I show that this unexpected separability can be understood in terms of a symmetry described by a conformal Killing tensor on a four dimensional spacetime obtained by a Kaluza-Klein reduction of the original black ring spacetime.
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Cook, William. "Numerical relativity in higher dimensional spacetimes." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/277718.

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The study of general relativity in higher dimensions has proven to be a fruitful avenue of research, revealing new applications of the theory, for instance in understanding strongly coupled quantum field theories through the holographic principle, and proposing an explanation of the hierarchy problem through TeV gravity scenarios. To understand the non-linear regime of higher dimensional general relativity, such as that involved in the merger of black holes, we use numerical relativity to solve the Einstein equations. In this thesis we develop and demonstrate several diagnostic tools and new initial data for use in numerical relativity simulations of higher dimensional spacetimes, and use these to investigate binary black hole systems. Firstly, we present a formalism for calculating the gravitational waves in a numerical simulation of a higher dimensional spacetime, and apply this formalism to the example of the head on merger of two equal mass black holes. In doing so, we simulate the merger of black holes in up to 10 spacetime dimensions for the first time, and investigate the dependence of the energy radiated away in gravitational waves on the number of dimensions. We also apply this formalism to the example of head on unequal mass black hole collisions, investigating the dependence of radiated energy and momentum on the number of dimensions and the mass ratio. This study complements and sheds further light on previous work on the merger of point particles with black holes in higher dimensions, and presents evidence for a link between the regime studied, and the large $D$ regime of general relativity where $D$ is the number of spacetime dimensions. We also present initial data that enables us to study black holes with initial momentum and angular momentum, putting in place the framework needed to study problems such as the scattering cross section of black holes in higher dimensions, and the nature of black hole orbits in higher dimensions. Finally, we present, and demonstrate the use of, an apparent horizon finder for higher dimensional spacetimes. This allows us to calculate a black hole's mass and spin, which characterise the black hole.
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Shaker, Jomaa K. M. A. "Algebraic computing in general relativity and supergravity : space-time embeddings and higher dimensional theories." Thesis, Imperial College London, 1985. http://hdl.handle.net/10044/1/37849.

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Di, Dato Adriana. "Correspondences in higher-dimensional gravity." Doctoral thesis, Universitat de Barcelona, 2015. http://hdl.handle.net/10803/384541.

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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.
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Kunesch, Markus. "Numerical simulations of instabilities in general relativity." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/283135.

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General relativity, one of the pillars of our understanding of the universe, has been a remarkably successful theory. It has stood the test of time for more than 100 years and has passed all experimental tests so far. Most recently, the LIGO collaboration made the first-ever direct detection of gravitational waves, confirming a long-standing prediction of general relativity. Despite this, several fundamental mathematical questions remain unanswered, many of which relate to the global existence and the stability of solutions to Einstein's equations. This thesis presents our efforts to use numerical relativity to investigate some of these questions. We present a complete picture of the end points of black ring instabilities in five dimensions. Fat rings collapse to Myers-Perry black holes. For intermediate rings, we discover a previously unknown instability that stretches the ring without changing its thickness and causes it to collapse to a Myers-Perry black hole. Most importantly, however, we find that for very thin rings, the Gregory-Laflamme instability dominates and causes the ring to break. This provides the first concrete evidence that in higher dimensions, the weak cosmic censorship conjecture may be violated even in asymptotically flat spacetimes. For Myers-Perry black holes, we investigate instabilities in five and six dimensions. In six dimensions, we demonstrate that both axisymmetric and non-axisymmetric instabilities can cause the black hole to pinch off, and we study the approach to the naked singularity in detail. Another question that has attracted intense interest recently is the instability of anti-de Sitter space. In this thesis, we explore how breaking spherical symmetry in gravitational collapse in anti-de Sitter space affects black hole formation. These findings were made possible by our new open source general relativity code, GRChombo, whose adaptive mesh capabilities allow accurate simulations of phenomena in which new length scales are produced dynamically. In this thesis, we describe GRChombo in detail, and analyse its performance on the latest supercomputers. Furthermore, we outline numerical advances that were necessary for simulating higher dimensional black holes stably and efficiently.
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Seahra, Sanjeev. "Physics in Higher-Dimensional Manifolds." Thesis, University of Waterloo, 2003. http://hdl.handle.net/10012/1276.

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In this thesis, we study various aspects of physics in higher-dimensional manifolds involving a single extra dimension. After giving some historical perspective on the motivation for studying higher-dimensional theories of physics, we describe classical tests for a non-compact extra dimension utilizing test particles and pointlike gyroscopes. We then turn our attention to the problem of embedding any given n-dimensional spacetime within an (n+1)-dimensional manifold, paying special attention to how any structure from the extra dimension modifies the standard n-dimensional Einstein equations. Using results derived from this investigation and the formalism derived for test particles and gyroscopes, we systematically introduce three specific higher-dimensional models and classify their properties; including the Space-Time-Matter and two types of braneworld models. The remainder of the thesis concentrates on specific higher-dimensional cosmological models drawn from the above mentioned scenarios; including an analysis of the embedding of Friedmann-Lemaitre-Robertson-Walker submanifolds in 5-dimensional Minkowski and topological Schwarzschild spaces, and an investigation of the dynamics of a d-brane that takes the form of a thin shell encircling a (d+2)-dimensional topological black hole in anti-deSitter space. The latter is derived from a finite-dimensional action principle, which allows us to consider the canonical quantization of the model and the solutions of the resulting Wheeler-DeWitt equation.
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Carter, Benedict Miles Nicholas. "Higher Dimensional Gravity, Black Holes and Brane Worlds." Thesis, University of Canterbury. Physics and Astronomy, 2006. http://hdl.handle.net/10092/1273.

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Current research is focussed on extending our knowledge of how gravity behaves on small scales and near black hole horizons, with various modifications which may probe the low energy limits of quantum gravity. This thesis is concerned with such modifications to gravity and their implications. In chapter two thermodynamical stability analyses are performed on higher dimensional Kerr anti de Sitter black holes. We find conditions for the black holes to be able to be in thermal equilibrium with their surroundings and for the background to be stable against classical tensor perturbations. In chapter three new spherically symmetric gravastar solutions, stable to radial perturbations, are found by utilising the construction of Visser and Wiltshire. The solutions possess an anti de Sitter or de Sitter interior and a Schwarzschild (anti) de Sitter or Reissner Nordstrom exterior. We find a wide range of parameters which allow stable gravastar solutions, and present the different qualitative behaviors of the equation of state for these parameters. In chapter four a six dimensional warped brane world compactification of the Salam-Sezgin supergravity model is constructed by generalizing an earlier hybrid Kaluza Klein / Randall Sundrum construction. We demonstrate that the model reproduces localized gravity on the brane in the expected form of a Newtonian potential with Yukawa type corrections. We show that allowed parameter ranges include values which potentially solve the hierarchy problem. The class of solutions given applies to Ricci flat geometries in four dimensions, and consequently includes brane world realisations of the Schwarzschild and Kerr black holes as particular examples. Arguments are given which suggest that the hybrid compactification of the Salam Sezgin model can be extended to reductions to arbitrary Einstein space geometries in four dimensions. This work furthers our understanding of higher dimensional general relativity, which is potentially interesting given the possibility that higher dimensions may become observable at the TeV scale, which will be probed in the Large Hadron Collider in the next few years.
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Godazgar, Mohammad Mahdi. "Aspects of higher dimensional Einstein theory and M-theory." Thesis, University of Cambridge, 2012. https://www.repository.cam.ac.uk/handle/1810/245148.

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This thesis contains two main themes. The first is Einstein's theory of general relativity in higher dimensions, while the second is M-theory. The first part of the thesis concerns the use of classification techniques based on the Weyl curvature in an attempt to systematically study higher dimensional general relativity and its solutions. After a review of the various classification schemes, the application of these schemes to the study of higher dimensional solutions is explained. The first application of the tensor approach that is discussed is the systematic classification of higher dimensional axisymmetric solutions. A complete classification of all algebraically special axisymmetric solutions to the vacuum Einstein equation in higher dimensions is presented. Next, the study of perturbations of higher dimensional solutions within this framework and the possibility of decoupling equations for black hole solutions of interest, as has been successfully done in four dimensions, is considered. In the case where such a decoupling of the perturbations is possible, a map for constructing solutions of the perturbation equation is presented and is applied to the Kerr/CFT correspondence. Also, the property of gravitational radiation emitted from an isolated source in higher dimensions is considered and the tensor classification scheme is used to derive the peeling property of the Weyl tensor in higher dimensions. This is shown to be different to that which occurs in four dimensions. Finally, after an in-depth exposition of the spinor classification scheme and its relation to the tensor approach, solutions belonging to the most special type in the spinor classification are classified. In addition, the classification of the black ring in this scheme is discussed. The second part of the thesis explores the use of generalised geometry as a tool for better understanding M-theory. After briefly reviewing the curious phenomenon of M-theory dualities, it is explained how generalised geometry can be used to show that these symmetries are not exclusive to compactifications of the theory, but can be made manifest without recourse to compactification. Finally, results regarding the local symmetries of M-theory in the generalised geometry framework for a particular symmetry group are presented.
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Schlue, Volker. "Linear waves on higher dimensional Schwarzschild black holes and Schwarzschild de Sitter spacetimes." Thesis, University of Cambridge, 2012. https://www.repository.cam.ac.uk/handle/1810/243640.

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I study linear waves on higher dimensional Schwarzschild black holes and Schwarzschild de Sitter spacetimes. In the first part of this thesis two decay results are proven for general finite energy solutions to the linear wave equation on higher dimensional Schwarzschild black holes. I establish uniform energy decay and improved interior first order energy decay in all dimensions with rates in accordance with the 3 + 1-dimensional case. The method of proof departs from earlier work on this problem. I apply and extend the new physical space approach to decay of Dafermos and Rodnianski. An integrated local energy decay estimate for the wave equation on higher dimensional Schwarzschild black holes is proven. In the second part of this thesis the global study of solutions to the linear wave equation on expanding de Sitter and Schwarzschild de Sitter spacetimes is initiated. I show that finite energy solutions to the initial value problem are globally bounded and have a limit on the future boundary that can be viewed as a function on the standard cylinder. Both problems are related to the Cauchy problem in General Relativity.
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Newsome, Ian M. "GEODESIC STRUCTURE IN SCHWARZSCHILD GEOMETRY WITH EXTENSIONS IN HIGHER DIMENSIONAL SPACETIMES." VCU Scholars Compass, 2018. https://scholarscompass.vcu.edu/etd/5414.

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From Birkoff's theorem, the geometry in four spacetime dimensions outside a spherically symmetric and static, gravitating source must be given by the Schwarzschild metric. This metric therefore satisfies the Einstein vacuum equations. If the mass which gives rise to the Schwarzschild spacetime geometry is concentrated within a radius of r=2M, a black hole will form. Non-accelerating particles (freely falling) traveling through this geometry will do so along parametrized curves called geodesics, which are curved space generalizations of straight paths. These geodesics can be found by solving the geodesic equation. In this thesis, the geodesic structure in the Schwarzschild geometry is investigated with an attempt to generalize the solution to higher dimensions.
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Books on the topic "Higher dimensional General Relativity"

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Horowitz, Gary T. Black holes in higher dimensions. New York: Cambridge University Press, 2012.

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1954-, Peternell Th, ed. Geometry of higher dimensional algebraic varieties. Basel: Birkhäuser Verlag, 1997.

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Fonseca, Carlos M. da. A panorama of mathematics: Pure and applied : Conference on Mathematics and Its Applications, November 14-17, 2014, Kuwait University, Safat, Kuwait. Providence, Rhode Island: American Mathematical Society, 2016.

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Block, Jonathan, 1960- editor of compilation, ed. String-Math 2011. Providence, Rhode Island: American Mathematical Society, 2012.

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editor, Bouchard Vincent 1979, ed. String-Math 2014: June 9-13, 2014, University of Alberta, Alberta, Canada. Providence, Rhode Island: American Mathematical Society, 2016.

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editor, Donagi Ron, Douglas, Michael (Michael R.), editor, Kamenova Ljudmila 1978 editor, and Roček M. (Martin) editor, eds. String-Math 2013: Conference, June 17-21, 2013, Simons Center for Geometry and Physics, Stony Brook, NY. Providence, Rhode Island: American Mathematical Society, 2014.

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P, Minicozzi William, ed. A course in minimal surfaces. Providence, R.I: American Mathematical Society, 2011.

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editor, Donagi Ron, Katz Sheldon 1956 editor, Klemm Albrecht 1960 editor, and Morrison, David R., 1955- editor, eds. String-Math 2012: July 16-21, 2012, Universität Bonn, Bonn, Germany. Providence, Rhode Island: American Mathematical Society, 2015.

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1932-, Bass Hyman, and Lam, T. Y. (Tsit-Yuen), 1942-, eds. Algebra. Providence, R.I: American Mathematical Society, 2010.

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Tsfasman, M. A. Algebraic geometry codes: Basic notions. Providence, R.I: American Mathematical Society, 2007.

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Book chapters on the topic "Higher dimensional General Relativity"

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Reall, Harvey S. "Higher-Dimensional Black Holes." In General Relativity, Cosmology and Astrophysics, 245–60. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-06349-2_12.

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LukÁcs, B. "Acausality and Retrocausality in Four- and Higher-Dimensional General Relativity." In The Nature of Time: Geometry, Physics and Perception, 277–88. Dordrecht: Springer Netherlands, 2003. http://dx.doi.org/10.1007/978-94-010-0155-7_29.

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del Castillo, Gerardo F. Torres. "Applications to General Relativity." In Spinors in Four-Dimensional Spaces, 103–47. Boston, MA: Birkhäuser Boston, 2010. http://dx.doi.org/10.1007/978-0-8176-4984-5_3.

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Drábek, Pavel, Hans P. Heinig, and Alois Kufner. "Higher dimensional Hardy inequality." In General Inequalities 7, 3–16. Basel: Birkhäuser Basel, 1997. http://dx.doi.org/10.1007/978-3-0348-8942-1_1.

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Compère, Geoffrey. "Three Dimensional Einstein’s Gravity." In Advanced Lectures on General Relativity, 35–79. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-04260-8_2.

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Klemm, D. "Review of Four-Dimensional Supersymmetric AdS Black Holes." In Recent Developments in General Relativity, 411–18. Milano: Springer Milan, 2000. http://dx.doi.org/10.1007/978-88-470-2113-6_34.

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Menotti, P. "Hamiltonian Structure of 2+1 Dimensional Gravity." In Recent Developments in General Relativity, Genoa 2000, 165–77. Milano: Springer Milan, 2002. http://dx.doi.org/10.1007/978-88-470-2101-3_12.

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Kamenshchik, Alexander Yu. "The Bianchi Classification of the Three-Dimensional Lie Algebras and Homogeneous Cosmologies and the Mixmaster Universe." In Einstein Equations: Physical and Mathematical Aspects of General Relativity, 93–137. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-18061-4_3.

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Hacon, Christopher. "Higher dimensional minimal model program for varieties of log general type." In Analytic and Algebraic Geometry, 525–55. Providence, Rhode Island: American Mathematical Society, 2010. http://dx.doi.org/10.1090/pcms/017/10.

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Lapidus, Michel L., Goran Radunović, and Darko Žubrinić. "Fractal Zeta Functions and Complex Dimensions: A General Higher-Dimensional Theory." In Fractal Geometry and Stochastics V, 229–57. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-18660-3_13.

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Conference papers on the topic "Higher dimensional General Relativity"

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REALL, HARVEY S. "HIGHER DIMENSIONAL BLACK HOLES." In Proceedings of the MG13 Meeting on General Relativity. WORLD SCIENTIFIC, 2015. http://dx.doi.org/10.1142/9789814623995_0007.

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Mbonye, Manasse R. "Evolution of evaporating Black Holes in a higher dimensional inflationary universe." In GENERAL RELATIVITY AND RELATIVISTIC ASTROPHYSICS. ASCE, 1999. http://dx.doi.org/10.1063/1.1301580.

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FUSTER, ANDREA, and NICOS PELAVAS. "HIGHER DIMENSIONAL VSI SPACETIMES AND SUPERGRAVITY." In Proceedings of the MG11 Meeting on General Relativity. World Scientific Publishing Company, 2008. http://dx.doi.org/10.1142/9789812834300_0136.

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ALIEV, ALIKRAM N. "HIGHER DIMENSIONAL ROTATING CHARGED BLACK HOLES." In Proceedings of the MG11 Meeting on General Relativity. World Scientific Publishing Company, 2008. http://dx.doi.org/10.1142/9789812834300_0157.

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SPERHAKE, ULRICH. "NUMERICAL RELATIVITY IN HIGHER DIMENSIONS." In Proceedings of the MG13 Meeting on General Relativity. WORLD SCIENTIFIC, 2015. http://dx.doi.org/10.1142/9789814623995_0025.

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DELSATE, TÉRENCE. "PHASES OF AdS HIGHER DIMENSIONAL BLACK STRINGS." In Proceedings of the MG12 Meeting on General Relativity. WORLD SCIENTIFIC, 2012. http://dx.doi.org/10.1142/9789814374552_0137.

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MAJUMDAR, ARCHAN S., and NUPUR MUKHERJEE. "GRAVITATIONAL LENSING BY HIGHER DIMENSIONAL BLACK HOLES." In Proceedings of the MG11 Meeting on General Relativity. World Scientific Publishing Company, 2008. http://dx.doi.org/10.1142/9789812834300_0237.

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Monteiro, Filipe C. P., and José P. S. Lemos. "The Shapiro time delay effect in higher dimensional general relativity." In Proceedings of the MG14 Meeting on General Relativity. WORLD SCIENTIFIC, 2017. http://dx.doi.org/10.1142/9789813226609_0309.

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MENA, FILIPE C., J. NATÁRIO, and P. TOD. "GRAVITATIONAL COLLAPSE TO HIGHER DIMENSIONAL TOPOLOGICAL BLACK HOLES." In Proceedings of the MG12 Meeting on General Relativity. WORLD SCIENTIFIC, 2012. http://dx.doi.org/10.1142/9789814374552_0130.

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KUNDURI, HARI K., JAMES LUCIETTI, and HARVEY S. REALL. "GRAVITATIONAL PERTURBATIONS OF HIGHER DIMENSIONAL ROTATING BLACK HOLES." In Proceedings of the MG11 Meeting on General Relativity. World Scientific Publishing Company, 2008. http://dx.doi.org/10.1142/9789812834300_0151.

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Reports on the topic "Higher dimensional General Relativity"

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Russo, David, and William A. Jury. Characterization of Preferential Flow in Spatially Variable Unsaturated Field Soils. United States Department of Agriculture, October 2001. http://dx.doi.org/10.32747/2001.7580681.bard.

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Abstract:
Preferential flow appears to be the rule rather than the exception in field soils and should be considered in the quantitative description of solute transport in the unsaturated zone of heterogeneous formations on the field scale. This study focused on both experimental monitoring and computer simulations to identify important features of preferential flow in the natural environment. The specific objectives of this research were: (1) To conduct dye tracing and multiple tracer experiments on undisturbed field plots to reveal information about the flow velocity, spatial prevalence, and time evolution of a preferential flow event; (2) To conduct numerical experiments to determine (i) whether preferential flow observations are consistent with the Richards flow equation; and (ii) whether volume averaging over a domain experiencing preferential flow is possible; (3) To develop a stochastic or a transfer function model that incorporates preferential flow. Regarding our field work, we succeeded to develop a new method for detecting flow patterns faithfully representing the movement of water flow paths in structured and non-structured soils. The method which is based on application of ammonium carbonate was tested in a laboratory study. Its use to detect preferential flow was also illustrated in a field experiment. It was shown that ammonium carbonate is a more conservative tracer of the water front than the popular Brilliant Blue. In our detailed field experiments we also succeeded to document the occurrence of preferential flow during soil water redistribution following the cessation of precipitation in several structureless field soils. Symptoms of the unstable flow observed included vertical fingers 20 - 60 cm wide, isolated patches, and highly concentrated areas of the tracers in the transmission zone. Soil moisture and tracer measurements revealed that the redistribution flow became fingered following a reversal of matric potential gradient within the wetted area. Regarding our simulation work, we succeeded to develop, implement and test a finite- difference, numerical scheme for solving the equations governing flow and transport in three-dimensional, heterogeneous, bimodal, flow domains with highly contrasting soil materials. Results of our simulations demonstrated that under steady-state flow conditions, the embedded clay lenses (with very low conductivity) in bimodal formations may induce preferential flow, and, consequently, may enhance considerably both the solute spreading and the skewing of the solute breakthrough curves. On the other hand, under transient flow conditions associated with substantial redistribution periods with diminishing water saturation, the effect of the embedded clay lenses on the flow and the transport might diminish substantially. Regarding our stochastic modeling effort, we succeeded to develop a theoretical framework for flow and transport in bimodal, heterogeneous, unsaturated formations, based on a stochastic continuum presentation of the flow and a general Lagrangian description of the transport. Results of our analysis show that, generally, a bimodal distribution of the formation properties, characterized by a relatively complex spatial correlation structure, contributes to the variability in water velocity and, consequently, may considerably enhance solute spreading. This applies especially in formations in which: (i) the correlation length scales and the variances of the soil properties associated with the embedded soil are much larger than those of the background soil; (ii) the contrast between mean properties of the two subdomains is large; (iii) mean water saturation is relatively small; and (iv) the volume fraction of the flow domain occupied by the embedded soil is relatively large.
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