Einstein equation at singularities

Ovidiu-Cristinel Stoica 1
  • 1 Faculty of Applied Sciences, University Politehnica of Bucharest, Splaiul Independentei nr. 313, sector 6, Bucharest, RO-060042, Romania

Abstract

Einstein’s equation is rewritten in an equivalent form, which remains valid at the singularities in some major cases. These cases include the Schwarzschild singularity, the Friedmann-Lemaître-Robertson-Walker Big Bang singularity, isotropic singularities, and a class of warped product singularities. This equation is constructed in terms of the Ricci part of the Riemann curvature (as the Kulkarni-Nomizu product between Einstein’s equation and the metric tensor).

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  • [1] C. Corda, H. J. M. Cuesta, Mod. Phys. Lett. A 25, 2423 (2010) http://dx.doi.org/10.1142/S0217732310033633

  • [2] R. Penrose, Phys. Rev. Lett. 14, 57 (1965) http://dx.doi.org/10.1103/PhysRevLett.14.57

  • [3] S. W. Hawking, P. Roy. Soc. A-Math. Phy. 294, 511 (1966) http://dx.doi.org/10.1098/rspa.1966.0221

  • [4] S. W. Hawking, P. Roy. Soc. A-Math. Phy. 295, 490 (1966) http://dx.doi.org/10.1098/rspa.1966.0255

  • [5] S. W. Hawking, P. Roy. Soc. A-Math. Phy. 300, 187 (1967) http://dx.doi.org/10.1098/rspa.1967.0164

  • [6] S. W. Hawking, R. W. Penrose, Proc. Roy. Soc. London Ser. A 314, 529 (1970) http://dx.doi.org/10.1098/rspa.1970.0021

  • [7] S. W. Hawking, G. F. R. Ellis, The Large Scale Structure of Space Time, (Cambridge University Press, 1995)

  • [8] O. C. Stoica, Ann. of Phys. 338, 186 (2013) http://dx.doi.org/10.1016/j.aop.2013.08.002

  • [9] I. M. Singer, J. A. Thorpe. The curvature of 4-dimensional Einstein spaces. In Global Analysis (Papers in Honor of K. Kodaira)

  • [10] Arthur L. Besse, Einstein Manifolds, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 10, (Berlin, New York, Springer-Verlag, 1987)

  • [11] S. Gallot, D. Hullin, J. Lafontaine, Riemannian Geometry, (Springer-Verlag, Berlin, New York, 3rd edition, 2004) http://dx.doi.org/10.1007/978-3-642-18855-8

  • [12] O. C. Stoica, arXiv:math.DG/1105.0201, To appear in Int. J. Geom. Methods Mod. Phys., (2011)

  • [13] O. C. Stoica, arXiv:math.DG/1105.3404, (2011)

  • [14] O. C. Stoica, An. St. Univ. Ovidius Constanta 20, 213 (2012)

  • [15] K. P. Tod, Class. Quant. Grav. 4, 1457 (1987) http://dx.doi.org/10.1088/0264-9381/4/5/038

  • [16] K. P. Tod, Class. Quant. Grav. 7, L13 (1990) http://dx.doi.org/10.1088/0264-9381/7/1/004

  • [17] K. P. Tod, Class. Quant. Grav. 8, L77 (1991) http://dx.doi.org/10.1088/0264-9381/8/4/002

  • [18] K. P. Tod, Rend. Sem. Mat. Univ. Politec. Torino 50, 69 (1992)

  • [19] K. P. Tod, The Conformal Structure of Space-Time, 123 (2002)

  • [20] K. P. Tod, Class. Quant. Grav. 20, 521 (2003) http://dx.doi.org/10.1088/0264-9381/20/3/309

  • [21] C. M. Claudel, K. P. Newman, P. Roy. Soc. A-Math. Phy. 454, 1073 (1998) http://dx.doi.org/10.1098/rspa.1998.0197

  • [22] K. Anguige, K. P. Tod, Ann. of Phys. 276, 257 (1999) http://dx.doi.org/10.1006/aphy.1999.5946

  • [23] K. Anguige, K. P. Tod, Ann. of Phys. 276, 294 (1999) http://dx.doi.org/10.1006/aphy.1999.5947

  • [24] B. O’Neill, Semi-Riemannian Geometry with Applications to Relativity. Number 103 in Pure Appl. Math., (Academic Press, New York-London, 1983)

  • [25] O. C. Stoica, Commun. Theor. Phys. 58, 613 (2012) http://dx.doi.org/10.1088/0253-6102/58/4/28

  • [26] A. S. Eddington, Nature 113, 192 (1924) http://dx.doi.org/10.1038/113192a0

  • [27] D. Finkelstein, Phys. Rev. 110, 965 (1958) http://dx.doi.org/10.1103/PhysRev.110.965

  • [28] O. C. Stoica, Eur. Phys. J. Plus 127, 1 (2012) http://dx.doi.org/10.1140/epjp/i2012-12083-1

  • [29] O. C. Stoica, Phys. Scr. 85, 055004 (2012) http://dx.doi.org/10.1088/0031-8949/85/05/055004

  • [30] O. C. Stoica, arXiv:gr-qc/1111.7082, To appear in U.P.B. Sci. Bull., Series A, (2013)

  • [31] O. C. Stoica, The International Conference of Differential Geometry and Dynamical Systems, arXiv:grqc/1112.4508, (2013)

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