Mohajan, Haradhan
(2013):
*Space-Time Singularities and Raychaudhuri Equations.*
Published in: Journal of Natural Sciences
, Vol. 1, No. 2
(31 December 2013): pp. 18-30.

Preview |
PDF
MPRA_paper_54069.pdf Download (170kB) | Preview |

## Abstract

Raychaudhuri equations play important roles to describe the gravitational focusing and space-time singularities. Amal Kumar Raychaudhuri established it in 1955 to describe gravitational focusing properties in cosmology. When the star is heavier than a few solar masses, it could undergo an endless gravitational collapse without achieving any equilibrium state. The final outcome of gravitational collapse of a massive star must necessarily be a black hole which covers the resulting space-time singularity and causal message from the singularity cannot reach the external observer at infinity. In this article Raychaudhuri equations are derived with the help of general relativity and topological properties. An attempt has been taken here to describe gravitational focusing and space-time singularities in some detail with easier mathematical calculations.

Item Type: | MPRA Paper |
---|---|

Original Title: | Space-Time Singularities and Raychaudhuri Equations |

English Title: | Space-Time Singularities and Raychaudhuri Equations |

Language: | English |

Keywords: | Gravitational focusing, Raychaudhuri equations, singularities. |

Subjects: | C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods |

Item ID: | 54069 |

Depositing User: | Haradhan Kumar Mohajan |

Date Deposited: | 03 Mar 2014 01:36 |

Last Modified: | 27 Sep 2019 20:55 |

References: | [1] Carroll, S. M. (2004). Space-time and Geometry: An Introduction to General Relativity. San Francisco: Addison-Wesley. [2] Hawking, S.W. and Ellis, G.F.R. (1973). The Large Scale Structure of Space-time, Cambridge University Press, Cambridge. [3] Hawking, S.W. and Penrose, R. (1970). The Singularities of Gravitational Collapse and Cosmology, Proceedings of the Royal Society, London, A314: 529–548. [4] Joshi P.S. (1993). Global Aspects in Gravitation and Cosmology, Clarendon Press, Oxford. [5] Poisson, E. (2004). A Relativist’s Toolkit: The Mathematics of Black Hole Mechanics. Cambridge: Cambridge University Press. [6] Raychaudhuri, A.K. (1955). Relativistic Cosmology, Physical Review, 98(4): 1123–1126. [7] Landau, L. and Lifshitz, E. M. (1975). Classical theory of fields, Pergamon Press, Oxford, UK. [8] Stephani, H.; Kramer, D.; MacCallum, M.; Hoenselaers, C.; Hertl, E. (2003). Exact Solutions to Einstein's Field Equations (2nd ed.), Cambridge: Cambridge University Press. [9] Kruskal, M.D. (1960). Maximal Extension of Schwarzschild Metric, Physical Review, 119(5): 1743–1745. [10] Szekeres, G. (1960). On the Singularities of a Riemannian Manifold, Publ. Math. Debrecen. 7: 285–301. [11] Mohajan H.K. (2013b). Schwarzschild Geometry from Exact Solution of Einstein Equation, Journal of Environmental Treatment Techniques, 1(2): 69–75. [12] Metev, S.M. and Veiko, V.P., Laser Assisted Microtechnology, 2nd ed., R. M. Osgood, Jr., Ed. Berlin, Germany: Springer-Verlag, 1998. [13] Mohajan H.K. (2013a). Singularity Theorems in General Relativity, M. Phil. Dissertation, Lambert Academic Publishing, Germany. [14] Kar, S. and SenGupta, S. (2007). The Raychaudhuri Equations: A Brief Review, Pramana Journal of Physics, Indian Academy of Sciences, 69(1): 49–76. [15] Tipler, F. (1977), Singularities and causality violation, Annals of Physics, 108(1): 1–36. |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/54069 |