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Relevant bibliographies by topics / Singularities (Mathematics) Einstein field equations

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Academic literature on the topic 'Singularities (Mathematics) Einstein field equations'

Author: Grafiati

Published: 4 June 2021

Last updated: 15 February 2022

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Journal articles on the topic "Singularities (Mathematics) Einstein field equations"

1

FEOLI, A. "A REGULARIZED SOLUTION OF THE LINEARIZED EINSTEIN EQUATIONS." International Journal of Modern Physics D 16, no. 01 (2007): 93–104. http://dx.doi.org/10.1142/s0218271807009334.

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Given a suitable energy density distribution, we find a solution of the linearized field equations of General Relativity that has some properties required by Einstein to be interpreted as a classical model of an extended elementary particle. It is spherically symmetric, free from singularities, smoothly connected with the outside linearized Schwarzschild solution and leads to a sort of "gravitational asymptotic freedom" in the limit r → 0. The case of a strong gravitational field is also studied with a numerical approach and the smooth behavior of the solution does not change.

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2

Kiessling, Michael K. H., and A. Shadi Tahvildar-Zadeh. "The Einstein–Infeld–Hoffmann legacy in mathematical relativity I: The classical motion of charged point particles." International Journal of Modern Physics D 28, no. 11 (2019): 1930017. http://dx.doi.org/10.1142/s0218271819300179.

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Einstein, Infeld and Hoffmann (EIH) claimed that the field equations of general relativity theory alone imply the equations of motion of neutral matter particles, viewed as point singularities in space-like slices of spacetime; they also claimed that they had generalized their results to charged point singularities. While their analysis falls apart upon closer scrutiny, the key idea merits our attention. This report identifies necessary conditions for a well-defined general-relativistic joint initial value problem of [Formula: see text] classical point charges and their electromagnetic and gra

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3

CHAN, R., M. F. A. DA SILVA, and JAIME F. VILLAS DA ROCHA. "GRAVITATIONAL COLLAPSE OF SELF-SIMILAR AND SHEAR-FREE FLUID WITH HEAT FLOW." International Journal of Modern Physics D 12, no. 03 (2003): 347–68. http://dx.doi.org/10.1142/s021827180300327x.

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A class of solutions to Einstein field equations is studied, which represents gravitational collapse of thick spherical shells made of self-similar and shear-free fluid with heat flow. It is shown that such shells satisfy all the energy conditions, and the corresponding collapse always forms naked singularities.

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4

Kong, DeXing, KeFeng Liu, and Ming Shen. "Time-periodic solutions of the Einstein’s field equations II: geometric singularities." Science China Mathematics 53, no. 6 (2010): 1507–20. http://dx.doi.org/10.1007/s11425-009-3164-y.

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Kong, DeXing, KeFeng Liu, and Ming Shen. "Time-periodic solutions of the Einstein’s field equations III: physical singularities." Science China Mathematics 54, no. 1 (2010): 23–33. http://dx.doi.org/10.1007/s11425-010-4003-x.

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GHOSH, S. G., D. W. DESHKAR, and N. N. SASTE. "FIVE-DIMENSIONAL DUST COLLAPSE WITH COSMOLOGICAL CONSTANT." International Journal of Modern Physics D 16, no. 01 (2007): 53–64. http://dx.doi.org/10.1142/s0218271807009309.

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We study the five-dimensional spherical collapse of an inhomogeneous dust in the presence of a positive cosmological constant. The general interior solutions, in the closed form, of the Einstein field equations, i.e. the 5D Tolman–Bondi–de Sitter, is obtained which in turn is matched to the exterior 5D Schwarzschild–de Sitter. It turns out that the collapse proceeds in the same way as in the Minkowski background, i.e. the strong curvature naked singularities form and thus violate the cosmic censorship conjecture. A brief discussion on the causal structure singularities and horizons is also giv

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7

Mena, Filipe C. "Spacetime Junctions and the Collapse to Black Holes in Higher Dimensions." Advances in Mathematical Physics 2012 (2012): 1–14. http://dx.doi.org/10.1155/2012/638726.

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We review recent results about the modelling of gravitational collapse to black holes in higher dimensions. The models are constructed through the junction of two exact solutions of the Einstein field equations: an interior collapsing fluid solution and a vacuum exterior solution. The vacuum exterior solutions are either static or containing gravitational waves. We then review the global geometrical properties of the matched solutions which, besides black holes, may include the existence of naked singularities and wormholes. In the case of radiating exteriors, we show that the data at the boun

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MARTINS, M. R., M. F. A. DA SILVA, and YUMEI WU. "COLLAPSING FLUID WITH SELF-SIMILARITY OF THE SECOND KIND IN 2 + 1 GRAVITY." International Journal of Modern Physics D 17, no. 05 (2008): 725–35. http://dx.doi.org/10.1142/s0218271808012462.

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Anisotropic fluid with self-similarity of the second kind in (2 + 1)-dimensional space–times with circular symmetry is studied. By imposing the condition that the radial pressure vanishes, we show that the only allowed solutions are the ones that represent dust fluid. All such solutions to the Einstein field equations are found and their local and global properties are studied in detail. It is found that some can be interpreted as representing gravitational collapse, in which both naked singularities and black holes can be formed.

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9

Winterberg, F. "Maxwell's Equations and Einstein-Gravity in the Planck Aether Model of a Unified Field Theory." Zeitschrift für Naturforschung A 45, no. 9-10 (1990): 1102–16. http://dx.doi.org/10.1515/zna-1990-9-1008.

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Abstract In the Planck aether substratum model it is assumed that space is densely filled with both positive and negative Planck masses described by a nonlinear nonrelativistic operator field equation. With-out expenditure of energy this substratum can form a lattice of vortex rings, with the vortex core radius equal the Planck length. The vortex ring radius is determined by a universal minimum energy quantum Reynolds number, making the ring radius and lattice spacing about 10 3 -10 4 times larger than the Planck length. The zero point fluctuations of the Planck masses bound in the vortex fila

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GONÇALVES, R. S., and JAIME F. VILLAS DA ROCHA. "N-DIMENSIONAL GRAVITATIONAL COLLAPSE WITH DARK ENERGY." International Journal of Modern Physics D 17, no. 08 (2008): 1295–309. http://dx.doi.org/10.1142/s0218271808012838.

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We study the evolution of an N-dimensional anisotropic fluid with kinematic self-similarity of the second kind and find a class of solutions to the Einstein field equations by assuming an equation of state where the radial pressure of the fluid is proportional to its energy density (pr= ωρ) and that the fluid moves along timelike geodesics. As in the four-dimensional case, the self-similarity requires ω = -1. The energy conditions and geometrical and physical properties of the solutions are studied. We find that, depending on the self-similar parameter α, they may represent black holes or nake

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Dissertations / Theses on the topic "Singularities (Mathematics) Einstein field equations"

1

Scott, Susan M. "New approaches to space-time singularities /." Title page, contents and abstract only, 1991. http://web4.library.adelaide.edu.au/theses/09PH/09phs429.pdf.

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Tziolas, Andreas Constantine Wang Anzhong. "Colliding branes and formation of spacetime singularities in superstring theory." Waco, Tex. : Baylor University, 2009. http://hdl.handle.net/2104/5334.

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Foster, Scott. "Singularity structure of scalar field cosmologies /." Title page, contents and abstract only, 1996. http://web4.library.adelaide.edu.au/theses/09PH/09phf757.pdf.

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Wang, Fang Ph D. Massachusetts Institute of Technology. "Radiation field for Einstein vacuum equations." Thesis, Massachusetts Institute of Technology, 2010. http://hdl.handle.net/1721.1/60203.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (p. 77-78).<br>The radiation field introduced by Friedlander provides a direct approach to the asymptotic expansion of solutions to the wave equation near null infinity. We use this concept to study the asymptotic behavior of solutions to the Einstein Vacuum equations, which are close to Minkowski space, at null infinity. By imposing harmonic gauge, the Einstein Vacuum equations reduce to a system of quasilinear wave equations on R"

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Gasperin, Garcia. "Applications of conformal methods to the analysis of global properties of solutions to the Einstein field equations." Thesis, Queen Mary, University of London, 2017. http://qmro.qmul.ac.uk/xmlui/handle/123456789/25820.

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Although the study of the initial value problem in General Relativity started in the decade of 1950 with the work of Foures-Bruhat, addressing the problem of global non-linear stability of solutions to the Einstein field equations is in general a hard problem. The first non-linear global stability result in General Relativity was obtained for the de-Sitter spacetime by means of the so-called conformal Einstein field equations introduced by H. Friedrich in the decade of 1980. The latter constitutes the main conceptual and technical tool for the results discussed in this thesis. In Chapter 1 the

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Van, der Walt Petrus Johannes. "Numerical relativity on cosmological past null cones." Thesis, Rhodes University, 2013. http://hdl.handle.net/10962/d1002959.

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The observational approach to cosmology is the endeavour to reconstruct the geometry of the Universe using only data that is theoretically verifiable within the causal boundaries of a cosmological observer. Using this approach, it was shown in [36] that given ideal cosmological observations, the only essential assumption necessary to determine the geometry of the Universe is a theory of gravity. Assuming General Relativity, the full set of Einstein field equations (EFEs) can be used to reconstruct the geometry of the Universe using direct observations on the past null cone (PNC) as initial con

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Cattoën, Céline. "Applied mathematics of space-time & space+time : problems in general relativity and cosmology : a thesis submitted to the Victoria University of Wellington in fulfilment of the requirements for the degree of Doctor of Philosophy in Mathematics /." ResearchArchive@Victoria e-thesis, 2009. http://hdl.handle.net/10063/972.

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Scott, Susan M. (Susan Marjorie). "New approaches to space-time singularities / by Susan M. Scott." 1991. http://hdl.handle.net/2440/19586.

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Includes bibliographical references<br>vi, 128 leaves ; 30 cm.<br>Title page, contents and abstract only. The complete thesis in print form is available from the University Library.<br>Thesis (Ph.D.)--University of Adelaide, Dept. of Physics and Mathematical Physics, 1992

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Mthethwa, Thulani Richard. "New classes of exact solutions for charged perfect fluids." Thesis, 2012. http://hdl.handle.net/10413/10533.

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We investigate techniques to generate new classes of exact solutions to the Einstein- Maxwell field equations which represent the gravitational field of charged perfect fluid spherically symmetric distributions of matter. Historically, a large number of solutions have been proposed but only a small number have been demonstrated to satisfy elementary conditions for physical acceptability. Firstly we examine the case of the constant density and constant electric field charged fluid sphere and show empirically that such configurations of matter are unlikely to exist as basic physical requir

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Kweyama, Mandlenkosi Christopher. "Analysis of shear-free spherically symmetric charged relativistic fluids." Thesis, 2011. http://hdl.handle.net/10413/5939.

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We study the evolution of shear-free spherically symmetric charged fluids in general relativity. This requires the analysis of the coupled Einstein-Maxwell system of equations. Within this framework, the master field equation to be integrated is yxx = f(x)y2 + g(x)y3 We undertake a comprehensive study of this equation using a variety of ap- proaches. Initially, we find a first integral using elementary techniques (subject to integrability conditions on the arbitrary functions f(x) and g(x)). As a re- sult, we are able to generate a class of new solutions containing, as special cases,

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Books on the topic "Singularities (Mathematics) Einstein field equations"

1

Bolejko, Krzysztof. Structures in the universe by exact methods: Formation, evolution, interactions. Cambridge University Press, 2010.

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2

Cox, Brian. Why Does E=mc2? DaCapo Press, 2009.

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Cox, Brian. Why does e=mc2: (and why should we care?). Da Capo Press, 2009.

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4

Carlos, Palenzuela-Luque, Bona-Casas C. (Carles), and SpringerLink (Online service), eds. Elements of numerical relativity and relativistic hydrodynamics: From Einstein's equations to astrophysical simulations. 2nd ed. Springer, 2009.

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5

Ellwood, D. (David), 1966- editor of compilation, Rodnianski, Igor, 1972- editor of compilation, Staffilani, Gigliola, 1966- editor of compilation, and Wunsch, Jared, editor of compilation, eds. Evolution equations: Clay Mathematics Institute Summer School, evolution equations, Eidgenössische Technische Hochschule, Zürich, Switzerland, June 23-July 18, 2008. American Mathematical Society, 2013.

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6

Zbigniew, Hajto, ed. Algebraic groups and differential Galois theory. American Mathematical Society, 2011.

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7

Shock-Wave Solutions Of The Einstein Equations With Perfect Fluid Sources: Existence And Consistency By A Locally Inertial Glimm Scheme (Memoirs of the American Mathematical Society). American Mathematical Society, 2004.

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8

Groah, Jeffrey, B. Temple, and Joel Smoller. Shock Wave Interactions in General Relativity: A Locally Inertial Glimm Scheme for Spherically Symmetric Spacetimes (Springer Monographs in Mathematics). Springer, 2006.

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1980-, Bolejko Krzysztof, ed. Structures in the universe by exact methods: Formation, evolution, interactions. Cambridge University Press, 2009.

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1980-, Bolejko Krzysztof, ed. Structures in the universe by exact methods: Formation, evolution, interactions. Cambridge University Press, 2009.

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Book chapters on the topic "Singularities (Mathematics) Einstein field equations"

1

Buchbinder, Iosif L., and Ilya L. Shapiro. "A brief review of general relativity." In Introduction to Quantum Field Theory with Applications to Quantum Gravity. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198838319.003.0011.

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The first chapter in Part II contains basic information on general relativity and all necessary notations and formulas. The consideration is concise but rather brief; it is not meant to replace a textbook on general relativity. Covariant derivatives, curvature tensors, Bianchi identities, covariant equations, the classical limit and Einstein equations are covered. The fact that the Schwarzschild solution and the cosmological solution contain singularities, which can be interpreted as indicating a need for quantum gravitational theory, is addressed. In addition, the applicability of general relativity and Planck units are discussed.

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2

Freeman, Richard, James King, and Gregory Lafyatis. "Introduction to Special Relativity." In Electromagnetic Radiation. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198726500.003.0005.

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The history of experiments and the development of the concepts of special relativity is presented with an emphasis on Einstein’s postulates of relativity and the relativity of simultaneity. The development of the Lorentz transformations follows Einstein’s work in enunciating the principles of covariance among inertial frames. The mathematics of the geometry of space-time is presented using Miniowski’s space-time diagrams. In developing Einstein’s argument for the reality of special relativity consequences, two examples of apparent paradoxes with their resolution are given: the twin and connected rocket problems. The mathematics of 4-vectors is developed with explicit presentation of the 4-vector gradient, 4-vector velocity, 4-vector momentum, 4-vector force, 4-wavevector, 4-current density, and 4-potential. This section sums up with the manifest covariance of Maxwell’s equations, and the presentation of the electromagnetic field and Einstein stress-energy tensor. Finally, simple examples of electromagnetic field transformation are given: static electric and magnetic fields parallel and transverse to the velocity relating two inertial frames; and the transformation of fields from a charge moving at relativistic velocities.

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