Relevant bibliographies by topics / Mathematical aspects of general relativity

Academic literature on the topic 'Mathematical aspects of general relativity'

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Published: 10 December 2022
Last updated: 28 January 2023

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Journal articles on the topic "Mathematical aspects of general relativity"

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Dafermos, Mihalis, James Isenberg, and Hans Ringström. "Mathematical Aspects of General Relativity." Oberwolfach Reports 9, no. 3 (2012): 2269–333. http://dx.doi.org/10.4171/owr/2012/37.

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Dafermos, Mihalis, James Isenberg, and Hans Ringström. "Mathematical Aspects of General Relativity." Oberwolfach Reports 12, no. 3 (2015): 1867–935. http://dx.doi.org/10.4171/owr/2015/33.

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Cederbaum, Carla, Mihalis Dafermos, James A. Isenberg, and Hans Ringström. "Mathematical Aspects of General Relativity." Oberwolfach Reports 18, no. 3 (November 25, 2022): 2157–267. http://dx.doi.org/10.4171/owr/2021/40.

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Seidel, Edward, and Wai-Mo Suen. "NUMERICAL RELATIVITY." International Journal of Modern Physics C 05, no. 02 (April 1994): 181–87. http://dx.doi.org/10.1142/s012918319400012x.

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The present status of numerical relativity is reviewed. There are five closely interconnected aspects of numerical relativity: (1) Formulation. The general covariant Einstein equations are reformulated in a way suitable for numerical study by separating the 4-dimensional spacetime into a 3-dimensional space evolving in time. (2) Techniques. A set of tools is developed for determining gauge choices, setting boundary and initial conditions, handling spacetime singularities, etc. As required by the special physical and mathematical properties of general relativity, such techniques are indispensable for the numerical evolutions of spacetime. (3) Coding. The optimal use of parallel processing is crucial for many problems in numerical relativity, due to the intrinsic complexity of the theory. (4) Visualization. Numerical relativity is about the evolutions of 3-dimensional geometric structures. There are special demands on visualization. (5) Interpretation and Understanding. The integration of numerical data in relativity into a consistent physical picture is complicated by gauge and coordinate degrees of freedoms and other difficulties. We give a brief overview of the progress made in these areas.
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Benedetto, Elmo, and Fabiano Feleppa. "Underlining some mathematical and physical aspects about the concept of motion in general relativity." Afrika Matematika 29, no. 3-4 (January 24, 2018): 349–56. http://dx.doi.org/10.1007/s13370-018-0545-9.

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GAMBINI, RODOLFO, and JORGE PULLIN. "CLASSICAL AND QUANTUM GENERAL RELATIVITY: A NEW PARADIGM." International Journal of Modern Physics D 14, no. 12 (December 2005): 2355–60. http://dx.doi.org/10.1142/s0218271805007917.

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We argue that recent developments in discretizations of classical and quantum gravity imply a new paradigm for doing research in these areas. The paradigm consists in discretizing the theory in such a way that the resulting discrete theory has no constraints. This solves many of the hard conceptual problems of quantum gravity. It also appears as a useful tool in some numerical simulations of interest in classical relativity. We outline some of the salient aspects and results of this new framework.
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Lin, De-Hone. "The 2+1-Dimensional Special Relativity." Symmetry 14, no. 11 (November 14, 2022): 2403. http://dx.doi.org/10.3390/sym14112403.

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In the new mathematical description of special relativity in terms of the relativistic velocity space, many physical aspects acquire new geometric meanings. Performing conformal deformations upon the 2-dimensional relativistic velocity space for the (2+1)-dimensional special relativity, we find that these conformal deformations correspond to the generalized Lorentz transformations, which are akin to the ordinary Lorentz transformation, but are morphed by a global rescaling of the polar angle and correspondingly characterized by a topological integral index. The generalized Lorentz transformations keep the two fundamental principles of special relativity intact, suggesting that the indexed generalization may be related to the Bondi–Metzner–Sachs (BMS) group of the asymptotic symmetries of the spacetime metric. Furthermore, we investigate the Doppler effect of light, the Planck photon rocket, and the Thomas precession, affirming that they all remain in the same forms of the standard special relativity under the generalized Lorentz transformation. Additionally, we obtain the general formula of the Thomas precession, which gives a clear geometric meaning from the perspective of the gauge field theory in the relativistic velocity space.
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Kolhe, K. G. "Relativity of Pseudo-Spherical Concept and Hartree-Fock Concept for Condensed Matter." International Journal for Research in Applied Science and Engineering Technology 10, no. 8 (August 31, 2022): 1839–41. http://dx.doi.org/10.22214/ijraset.2022.46529.

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Abstract: The function Fn,l (r) ;the radial part of of the pseudo-wave function k (r,  ,  ) is expressed in terms of ion-core electron density, n,l (r) and its relation with the radial part Pn,l (r ) of Hartree- Fock wave function. A new mathematical function psl (x) called as pseudo-spherical function has been developed which is similar to other mathematical functions, and helpful in determining many types of electron densities. The physical and mathematical developments on various aspects such as functional densities have been described. It is further emphasized that Fn,l (r) and Pn,l (r) functions and core electron density at different electronic states of the atom that both the functions posses strong correlationship. Study concludes that the present development resulted into an innovative simpler path in the orientation of condensed matter as well as Mathematical Physics.
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Giulini, Domenico. "Aspects of 3-manifold theory in classical and quantum general relativity." Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 86, no. 2 (September 19, 2016): 235–71. http://dx.doi.org/10.1007/s12188-016-0135-4.

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Vulcanov, Dumitru N., and Remus-Ştefan Ş. Boată. "Using Algebraic Computing To Teach General Relativity And Cosmology." Annals of West University of Timisoara - Physics 56, no. 1 (December 1, 2012): 139–44. http://dx.doi.org/10.1515/awutp-2015-0022.

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AbstractThe article presents some new aspects and experience on the use of computer in teaching general relativity and cosmology for undergraduate students (and not only) with some experience in computer manipulation. Some years ago certain results were reported [1] using old fashioned computer algebra platforms but the growing popularity of graphical platforms as Maple and Mathematica forced us to adapt and reconsider our methods and programs. We will describe some simple algebraic programming procedures (in Maple with GrTensorII package) for obtaining and the study of some exact solutions of the Einstein equations in order to convince a dedicated student in general relativity about the utility of a computer algebra system.
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Dissertations / Theses on the topic "Mathematical aspects of general relativity"

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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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Abdelfattah, Derhham. "General Relativity and penrose process." Master's thesis, University of Cape Town, 2016. http://hdl.handle.net/11427/28961.

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Rendall, Alan D. "Some aspects of curvature in general relativity." Thesis, University of Aberdeen, 1987. http://digitool.abdn.ac.uk/R?func=search-advanced-go&find_code1=WSN&request1=AAIU009831.

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The purpose of this thesis is to study in depth the relationship between the curvature of space-time and the other geometrical objects which naturally arise in general relativity. Most of the results obtained apply to the generic case. Chapter 1 contains a discussion of certain aspects of fibre bundle theory required in later chapters which may be unfamiliar to many relativists, while chapter 2 contains preliminary material on curvature in relativity and proves a continuity property of the algebraic classification of the Weyl and energy-momentum tensors. Chapter 3 describes the generic behaviour of the Riemann, Weyl and energy-momentum tensors, and chapter 5 goes on to use this description to investigate the relationship of the Riemann tensor to the metric, conformal class and connection of space-time in the generic case. In particular it is proved that the Riemann tensor uniquely and continuously determines the connections. The information obtained in chapter 3 on the algebraic type of curvature in the general case is related in chapter 4 to the topology of the underlying manifold. In chapter 6 a topology is defined on the set of sectional curvatures of all Lorentz metrics on a given manifold. The remainder of the chapter attempts to do for the sectional curvature what was done for the Riemann tensor in chapter 5 but, because sectional curvature is more difficult to handle, the results obtained are necessarily more modest.
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Keir, Joseph. "Aspects of stability and instability in general relativity." Thesis, University of Cambridge, 2016. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.709537.

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Sbierski, Jan. "On the initial value problem in general relativity and wave propagation in black-hole spacetimes." Thesis, University of Cambridge, 2014. https://www.repository.cam.ac.uk/handle/1810/248837.

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The first part of this thesis is concerned with the question of global uniqueness of solutions to the initial value problem in general relativity. In 1969, Choquet-Bruhat and Geroch proved, that in the class of globally hyperbolic Cauchy developments, there is a unique maximal Cauchy development. The original proof, however, has the peculiar feature that it appeals to Zorn’s lemma in order to guarantee the existence of this maximal development; in particular, the proof is not constructive. In the first part of this thesis we give a proof of the above mentioned theorem that avoids the use of Zorn’s lemma. The second part of this thesis investigates the behaviour of so-called Gaussian beam solutions of the wave equation - highly oscillatory and localised solutions which travel, for some time, along null geodesics. The main result of this part of the thesis is a characterisation of the temporal behaviour of the energy of such Gaussian beams in terms of the underlying null geodesic. We conclude by giving applications of this result to black hole spacetimes. Recalling that the wave equation can be considered a “poor man’s” linearisation of the Einstein equations, these applications are of interest for a better understanding of the black hole stability conjecture, which states that the exterior of our explicit black hole solutions is stable to small perturbations, while the interior is expected to be unstable. The last part of the thesis is concerned with the wave equation in the interior of a black hole. In particular, we show that under certain conditions on the black hole parameters, waves that are compactly supported on the event horizon, have finite energy near the Cauchy horizon. This result is again motivated by the investigation of the conjectured instability of the interior of our explicit black hole solutions.
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Cramer, Claes Richard. "Quantum aspects of time-machines." Thesis, University of York, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.265661.

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Watts, David G. "Inertial and electromagnetic aspects of matter induced from five-dimensional general relativity." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape9/PQDD_0008/NQ38281.pdf.

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Thillaisundaram, Ashok. "Aspects of fluid dynamics and the fluid/gravity correspondence." Thesis, University of Cambridge, 2017. https://www.repository.cam.ac.uk/handle/1810/267097.

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This thesis considers various extensions to the fluid/gravity correspondence as well as problems fundamental to the study of fluid dynamics. The fluid/gravity correspondence is a map between the solutions of the Navier-Stokes equations of fluid dynamics and the solutions of the Einstein equations in one higher spatial dimension. This map arose within the context of string theory and holography and is a specific realisation of a much wider class of dualities known as the Anti de Sitter/Conformal Field Theory (AdS/CFT) correspondence. The first chapter is an introduction; the second chapter reviews the fluid/gravity correspondence. The next two chapters extend existing work on the fluid/gravity map. Our first result concerns the fluid/gravity map for forced fluid dynamics in arbitrary spacetime dimensions. Forced fluid flows are of particular interest as they are known to demonstrate turbulent behaviour. For the case of a fluid with a dilaton-dependent forcing term, we present explicit expressions for the dual bulk metric, the fluid dynamical stress tensor and Lagrangian to second order in boundary spacetime derivatives. Our second result concerns fluid flows with multiple anomalous currents in the presence of external electromagnetic fields. It has recently been shown using thermodynamic arguments that the entropy current for such anomalous fluids contains additional first order terms proportional to the vorticity and magnetic field. Using the fluid/gravity map, we replicate this result using gravitational methods. The final two chapters consider questions related to the equations of fluid dynamics themselves; these chapters do not involve the fluid/gravity correspondence. The first of these chapters is a review of the various constraints that must be satisfied by the transport coefficients. In the final chapter, we derive the constraints obtained by requiring that the equilibrium fluid configurations are linearly stable to small perturbations. The inequalities that we obtain here are slightly weaker than those found by demanding that the divergence of the entropy current is non-negative.
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Flanagan, Eanna E. Thorne Kip S. "Topics in general relativity : the hoop conjecture and theoretical aspects of gravitational wave detection /." Diss., Pasadena, Calif. : California Institute of Technology, 1994. http://resolver.caltech.edu/CaltechETD:etd-11132006-095610.

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Cavalcanti, Rogério Teixeira. "Aspects of black hole physics beyond general relativity : extra dimensions, horizon wave function and applications." reponame:Repositório Institucional da UFABC, 2017.

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Orientador: Prof. Dr. Roldão da Rocha Jr.
Tese (doutorado) - Universidade Federal do ABC, Programa de Pós-Graduação em Física, 2017.
Neste trabalho foram investigadas algumas conseguências da física de buracos negros em teorias cujo domínio está além do domínio da relatividade geral, em especial em teorias efetivos com dimensões extras. A investigação foi em substancialmente conduzida baseando-se em três efeitos gravitacionais, a saber, a radiação Hawking, o regime de deflexão forte de lentes gravitacionais e a formação de buracos negros quânticos. Uma solução de modelo cosmológico imerso em uma brana espessa foi também investigada. Modelos e teorias efetivas fornecem meios para testar os limites de validade de teorias conhecidas e indicam o que deveríamos esperar além desses limites. Baseado nessa ideia foram usados alguns modelos efetivos para estudar efeitos não previstos pela relatividade geral, associados a cada um dos fenômenos mencionados.
This work is devoted to investigate some consequences of black holes physics beyond the domain of general relativity, mainly in effective extra dimensional models. The investigation is carried along three gravitational effects, namely the Hawking radiation, the strong deflection of gravitational lensing and the formation of quantum black holes. A cosmological thick brane solution is also investigated. Effective theories and models provide a prominent approach for testing the limits of known theories and show what would be expected beyond that. Based on such idea we have used effective models for finding deviations of general relativity associated to each of the mentioned phenomena.
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Books on the topic "Mathematical aspects of general relativity"

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Cacciatori, Sergio, Batu Güneysu, and Stefano Pigola, eds. Einstein Equations: Physical and Mathematical Aspects of General Relativity. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-18061-4.

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International Conference on Aspects of General Relativity and Mathematical Physics (1993 Mexico City, Mexico). Proceedings of the International Conference on Aspects of General Relativity and Mathematical Physics: June 2-4, 1993 at Centro de Investigación y de Estudios Avanzados del I.P.N., Mexico City. Mexico City: CINVESTAV, 1993.

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Samos Meeting on Cosmology, Geometry and Relativity (2nd 1998 Pythagoreon, Samos, Greece). Mathematical and quantum aspects of relativity and cosmology: Proceedings of the second Samos Meeting on Cosmology, Geometry and Relativity, held at Pythagoreon, Samos, Greece, 31 August-4 September 1998. Berlin: Springer, 2000.

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Mathematical problems of general relativity theory. Zu rich: European Mathematical Society, 2008.

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Straumann, Norbert. General Relativity. 2nd ed. Dordrecht: Springer Netherlands, 2013.

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Esposito, Giampiero. Complex general relativity. Dordrecht: Kluwer Academic Publishers, 1995.

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Rotating fields in general relativity. Cambridge [Cambridgeshire]: Cambridge University Press, 1985.

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Kotlikoff, Laurence J. On the general relativity of fiscal language. Cambridge, Mass: National Bureau of Economic Research, 2006.

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Das, Anadijiban. The general theory of relativity: A mathematical exposition. New York: Springer, 2012.

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Andrew, DeBenedictis, and SpringerLink (Online service), eds. The General Theory of Relativity: A Mathematical Exposition. New York, NY: Springer New York, 2012.

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Book chapters on the topic "Mathematical aspects of general relativity"

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De Falco, Vittorio. "Relativity of Observer Splitting Formalism and Some Astrophysical Applications." In Einstein Equations: Physical and Mathematical Aspects of General Relativity, 227–42. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-18061-4_7.

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Carlotto, Alessandro. "Four Lectures on Asymptotically Flat Riemannian Manifolds." In Einstein Equations: Physical and Mathematical Aspects of General Relativity, 3–59. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-18061-4_1.

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Ryzner, Jiří, and Martin Žofka. "Crystal Spacetimes with Discrete Translational Symmetry." In Einstein Equations: Physical and Mathematical Aspects of General Relativity, 289–312. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-18061-4_10.

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Veselý, Jiří, and Martin Žofka. "Electrogeodesics and Extremal Horizons in Kerr–Newman–(anti-)de Sitter." In Einstein Equations: Physical and Mathematical Aspects of General Relativity, 313–32. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-18061-4_11.

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Völkel, Sebastian H., and Kostas D. Kokkotas. "Hearing the Nature of Compact Objects." In Einstein Equations: Physical and Mathematical Aspects of General Relativity, 333–43. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-18061-4_12.

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Zampeli, Adamantia. "Minisuperspace Quantisation via Conditional Symmetries." In Einstein Equations: Physical and Mathematical Aspects of General Relativity, 345–57. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-18061-4_13.

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Finster, Felix. "Lectures on Linear Stability of Rotating Black Holes." In Einstein Equations: Physical and Mathematical Aspects of General Relativity, 61–91. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-18061-4_2.

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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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Cella, Giancarlo. "The Physics of LIGO–Virgo." In Einstein Equations: Physical and Mathematical Aspects of General Relativity, 139–83. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-18061-4_4.

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Bozzola, Gabriele, and Vasileios Paschalidis. "Generation of Initial Data for General-Relativistic Simulations of Charged Black Holes." In Einstein Equations: Physical and Mathematical Aspects of General Relativity, 187–95. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-18061-4_5.

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Conference papers on the topic "Mathematical aspects of general relativity"

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Carfora, Mauro. "Simplicial Aspects of String Dualities." In GENERAL RELATIVITY AND GRAVITATIONAL PHYSICS: 16th SIGRAV Conference on General Relativity and Gravitational Physics. AIP, 2005. http://dx.doi.org/10.1063/1.1891546.

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CHRISTODOULOU, DEMETRIOS. "THE FORMATION OF BLACK HOLES IN GENERAL RELATIVITY." In XVIth International Congress on Mathematical Physics. WORLD SCIENTIFIC, 2010. http://dx.doi.org/10.1142/9789814304634_0002.

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ACQUAVIVA, GIOVANNI. "THERMAL ASPECTS IN CURVED METRICS." In Proceedings of the MG13 Meeting on General Relativity. WORLD SCIENTIFIC, 2015. http://dx.doi.org/10.1142/9789814623995_0327.

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GUENDELMAN, EDUARDO I., and MAHARY VASIHOUN. "ASPECTS OF TWO MEASURES THEORY." In Proceedings of the MG13 Meeting on General Relativity. WORLD SCIENTIFIC, 2015. http://dx.doi.org/10.1142/9789814623995_0103.

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KLAINERMAN, SERGIU. "RECENT RESULTS IN MATHEMATICAL GR." In Proceedings of the MG13 Meeting on General Relativity. WORLD SCIENTIFIC, 2015. http://dx.doi.org/10.1142/9789814623995_0006.

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SHARIF, MUHAMMAD, and WAJIHA JAVED. "SOME INTERESTING ASPECTS OF HAWKING RADIATION." In Proceedings of the MG13 Meeting on General Relativity. WORLD SCIENTIFIC, 2015. http://dx.doi.org/10.1142/9789814623995_0325.

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BERGSHOEFF, ERIC A., JELLE HARTONG, TOMÁS ORTÍN, and DIEDERIK ROEST. "GLOBAL ASPECTS OF SEVEN–BRANE CONFIGURATIONS." In Proceedings of the MG11 Meeting on General Relativity. World Scientific Publishing Company, 2008. http://dx.doi.org/10.1142/9789812834300_0540.

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RINGSTRÖM, HANS. "On a wave map equation arising in general relativity." In XIVth International Congress on Mathematical Physics. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812704016_0031.

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KLEMAN, MAURICE. "SOME ASPECTS OF DEFECT THEORY IN SPACETIME." In Proceedings of the MG13 Meeting on General Relativity. WORLD SCIENTIFIC, 2015. http://dx.doi.org/10.1142/9789814623995_0489.

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ROMERO, C., and J. B. FORMIGA. "GEOMETRIC AND KINEMATICAL ASPECTS OF RINDLER OBSERVERS." In Proceedings of the MG11 Meeting on General Relativity. World Scientific Publishing Company, 2008. http://dx.doi.org/10.1142/9789812834300_0144.

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Reports on the topic "Mathematical aspects of general relativity"

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Saptsin, V., Володимир Миколайович Соловйов, and I. Stratychuk. Quantum econophysics – problems and new conceptions. КНУТД, 2012. http://dx.doi.org/10.31812/0564/1185.

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This article is dedicated to the econophysical analysis of conceptual fundamentals and mathematical apparatus of classical physics, relativity theory, non-relativistic and relativistic quantum mechanics. The historical and methodological aspects as well as the modern state of the problem of the socio-economic modeling are considered.
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Saptsin, Vladimir, and Володимир Миколайович Соловйов. Relativistic quantum econophysics – new paradigms in complex systems modelling. [б.в.], July 2009. http://dx.doi.org/10.31812/0564/1134.

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This work deals with the new, relativistic direction in quantum econophysics, within the bounds of which a change of the classical paradigms in mathematical modelling of socio-economic system is offered. Classical physics proceeds from the hypothesis that immediate values of all the physical quantities, characterizing system’s state, exist and can be accurately measured in principle. Non-relativistic quantum mechanics does not reject the existence of the immediate values of the classical physical quantities, nevertheless not each of them can be simultaneously measured (the uncertainty principle). Relativistic quantum mechanics rejects the existence of the immediate values of any physical quantity in principle, and consequently the notion of the system state, including the notion of the wave function, which becomes rigorously nondefinable. The task of this work consists in econophysical analysis of the conceptual fundamentals and mathematical apparatus of the classical physics, relativity theory, non-relativistic and relativistic quantum mechanics, subject to the historical, psychological and philosophical aspects and modern state of the socio-economic modeling problem. We have shown that actually and, virtually, a long time ago, new paradigms of modeling were accepted in the quantum theory, within the bounds of which the notion of the physical quantity operator becomes the primary fundamental conception(operator is a mathematical image of the procedure, the action), description of the system dynamics becomes discrete and approximate in its essence, prediction of the future, even in the rough, is actually impossible when setting aside the aftereffect i.e. the memory. In consideration of the analysis conducted in the work we suggest new paradigms of the economical-mathematical modeling.
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Hlushak, Oksana M., Svetlana O. Semenyaka, Volodymyr V. Proshkin, Stanislav V. Sapozhnykov, and Oksana S. Lytvyn. The usage of digital technologies in the university training of future bachelors (having been based on the data of mathematical subjects). [б. в.], July 2020. http://dx.doi.org/10.31812/123456789/3860.

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Abstract:
This article demonstrates that mathematics in the system of higher education has outgrown the status of the general education subject and should become an integral part of the professional training of future bachelors, including economists, on the basis of intersubject connection with special subjects. Such aspects as the importance of improving the scientific and methodological support of mathematical training of students by means of digital technologies are revealed. It is specified that in order to implement the task of qualified training of students learning econometrics and economic and mathematical modeling, it is necessary to use digital technologies in two directions: for the organization of electronic educational space and in the process of solving applied problems at the junction of the branches of economics and mathematics. The advantages of using e-learning courses in the educational process are presented (such as providing individualization of the educational process in accordance with the needs, characteristics and capabilities of students; improving the quality and efficiency of the educational process; ensuring systematic monitoring of the educational quality). The unified structures of “Econometrics”, “Economic and mathematical modeling” based on the Moodle platform are the following ones. The article presents the results of the pedagogical experiment on the attitude of students to the use of e-learning course (ELC) in the educational process of Borys Grinchenko Kyiv University and Alfred Nobel University (Dnipro city). We found that the following metrics need improvement: availability of time-appropriate mathematical materials; individual approach in training; students’ self-expression and the development of their creativity in the e-learning process. The following opportunities are brought to light the possibilities of digital technologies for the construction and research of econometric models (based on the problem of dependence of the level of the Ukrainian population employment). Various stages of building and testing of the econometric model are characterized: identification of variables, specification of the model, parameterization and verification of the statistical significance of the obtained results.
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