Relevant bibliographies by topics / 010504 Mathematical Aspects of General Relativity

Academic literature on the topic '010504 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 "010504 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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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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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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Nandi, Kamal K. "Some Aspects of Minimally Relativistic Newtonian Gravity." Zeitschrift für Naturforschung A 46, no. 12 (December 1, 1991): 1026–32. http://dx.doi.org/10.1515/zna-1991-1205.

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Abstract This paper aims to examine if the classical tests of General Relativity (GR) can be predicted by a simpler approach based on minimal changes in the Newtonian gravity. The approach yields a precession of the perihelion of Mercury by an amount 39.4"/century which is very close to the observed Dicke-Goldenberg value (39.6"/century), but less than the popularly accepted value (43"/ century). The other tests exactly coincide with those of GR. Our analysis also displays the genesis as well as the role of geometry in the description of gravitational processes. The time dependent spherically symmetric equations, which are mathematically interesting, call for a further study. The model also allows unambiguous formulation of conservation laws. On the whole, the paper illustrates the limited extent to which a second rank tensor analogy (nonlinear) with flat background Faraday-Maxwell electrodynamics can be pushed in describing gravitation
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MURDZEK, R. "THE GEOMETRY OF THE TORUS UNIVERSE." International Journal of Modern Physics D 16, no. 04 (April 2007): 681–86. http://dx.doi.org/10.1142/s0218271807009826.

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In this contribution, we show that the cyclic universe models naturally emerge from torus geometry in a braneworld scenario. The Riemannian metric on torus and the fundamental tensors of the General Relativity are derived. A discussion on particular aspects of this model is also given.
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Dissertations / Theses on the topic "010504 Mathematical Aspects of General Relativity"

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Boero, Ezequiel Fernando. "Lentes gravitacionales y modelos geométricos para el estudio de sistemas astrofı́sicos en el contexto cosmológico." Doctoral thesis, 2017. http://hdl.handle.net/11086/5841.

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Tesis (Doctor en Física)--Universidad Nacional de Córdoba, Facultad de Matemática, Astronomía, Física y Computación, 2017.
En esta tesis se abordan tres temáticas principales: el uso de modelos geométricos para la descripción de sistemas astrofísicos, el desarrollo de un nuevo formalismo en la teoría de lentes gravitacionales que extiende ideas de trabajos previos al contexto cosmológico y, por último, la cuestión de cómo realizar promedios en el marco de la relatividad general. Uno de los motivos principales que persigue este trabajo es el de discutir la forma en que el estudio del contenido de materia en el Universo es abordado. En particular, aquí indagamos nuevas posibilidades de descripción de la fenomenología asociada al problema de la masa faltante presentando nuevas herramientas desde el área de la teoría de lentes gravitacionales débiles sobre un espaciotiempo de fondo cosmológico. Las mismas permiten un modelado mucho más general de la geometría de la lente que aquellas que son habitualmente consideradas y se basan esencialmente en una concepción Newtoniana de la distribución de materia.
This doctorate thesis deals with three main topics: the use of geometric models for the description of astrophysical systems, the development of a new formalism within the theory of gravitational lensing which improves and generalize previous ideas already presented to the cosmological context and, finally the problem of how to perform averages in the conceptual framework of general relativity. One of the main motivation of this work is to discuss the way in which the study of the matter content in the Universe is addressed. In particular, here we investigate new possibilities of description of the phenomenology related to the missing mass problem. We present new tool from the subject of weak gravitational lensing over a cosmological background spacetime. Such tools allow a much more general modelling of the lens geometry than those that are usually considered and which are based essentially on a Newtonian concepton of the matter distribution.
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Books on the topic "010504 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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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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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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Mathematical Quantum Aspects of Relativity and Cosmology. Springer, 2000.

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Cotsakis, Spiros, and Gary W. Gibbons. Mathematical and Quantum Aspects of Relativity and Cosmology. Springer, 2010.

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Pigola, Stefano, Sergio Cacciatori, and Batu Güneysu. Einstein Equations : Physical and Mathematical Aspects of General Relativity: Domoschool 2018. Birkhäuser, 2019.

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Pigola, Stefano, Sergio Cacciatori, and Batu Güneysu. Einstein Equations : Physical and Mathematical Aspects of General Relativity: Domoschool 2018. Springer International Publishing AG, 2020.

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Mashhoon, Bahram. Extension of General Relativity. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198803805.003.0005.

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Nonlocal general relativity (GR) requires an extension of the mathematical framework of GR. Nonlocal GR is a tetrad theory such that the orthonormal tetrad frame field of a preferred set of observers carries the sixteen gravitational degrees of freedom. The spacetime metric is then defined via the orthonormality condition. The preferred frame field is used to define a new linear Weitzenböck connection in spacetime. The non-symmetric Weitzenböck connection is metric compatible, curvature-free and renders the preferred (fundamental) frame field parallel. This circumstance leads to teleparallelism. The fundamental parallel frame field defined by the Weitzenböck connection is the natural generalization of the parallel frame fields of the static inertial observers in a global inertial frame in Minkowski spacetime. The Riemannian curvature of the Levi-Civita connection and the torsion of the Weitzenböck connection are complementary aspects of the gravitational field in extended GR.
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Cotsakis, Spiros, and Gary W. Gibbons. 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. Springer London, Limited, 2008.

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Book chapters on the topic "010504 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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