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Abstract

GLOBAL HYPERBOLICITY IN SPACE-TIME MANIFOLD

Haradhan Kumar Mohajan

Assistant Professor, Faculty of Business Studies, Premier University, Chittagong, Bangladesh

14 - 30
Vol. 1, Issue 1, Jan-Jun, 2016
Receiving Date: 2015-10-30
Acceptance Date: 2016-01-12
Publication Date: 2016-01-19
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Abstract

Global hyperbolicity is the most important condition on causal structure space-time, which is involved in problems as cosmic censorship, predictability etc.


Keywords: Cauchy surface; causality; global hyperbolicity; space-time manifold; space-time singularities


References
  1. Bernal, A.N. and Sánchez, M. (2003), On Smooth Cauchy Hypersurfaces and Geroch‟s Splitting Theorem, Communications in Mathematical Physics, 243(3): 461–470.
  2. Bernal, A.N. and Sánchez, M. (2005), Smoothness of Time Functions and the Metric Splitting of Globally Hyperbolic Spacetimes, arXiv:gr-qc/0401112v3 15
  3. Clarke, C.J.S. (1986), Singularities: Global and Local Aspects in Topological Properties and Global Structure of Space-time (ed. P.G. Bergmann and V. de. Sabbata), Plenum Press, New York.
  4. Geroch, R.P. (1970), Domain of Dependence, Journal of Mathematical Physics, 11: 437–449
  5. Geroch, R.P.; Kronheimer, E.H. and Penrose, R. (GKP) (1972), Ideal Points in Space-time, Proceedings of the Royal Society, London, A 237: 545–567.
  6. Hawking, S.W. (1966a), The Occurrence of Singularities in Cosmology I, Proceedings of the Royal Society, London, A294: 511–521.
  7. Hawking, S.W. (1966b), The Occurrence of Singularities in Cosmology II, Proceedings of the Royal Society, London, A295: 490–493.
  8. Hawking, S.W. (1994), Classical Theory, arXiv:hep-th/9409195v1 30 Sep 1994
  9. Hawking, S.W. and Ellis, G.F.R. (1973), The Large Scale Structure of Space-time, Cambridge University Press, Cambridge
  10. Hawking, S.W. and Penrose, R. (1970), The Singularities of Gravitational Collapse and Cosmology, Proceedings of the Royal Society of London, Series A, Mathematical and Physical Sciences, 314: 529–548.
  11. Hawking, S.W. and Sachs, R.K. (1974), Causally Continuous Spacetimes, Communications in Mathematical Physics, 35: 287–296
  12. Joshi, P.S. (1996), Global Aspects in Gravitation and Cosmology, 2nd Edition, Clarendon Press, Oxford.
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  16. Mohajan, H.K. (2013a), Friedmann, Robertson-Walker (FRW) Models in Cosmology, Journal of Environmental Treatment Techniques, 1(3): 158–164.
  17. Mohajan, H.K. (2013b), Schwarzschild Geometry of Exact Solution of Einstein Equation in Cosmology, Journal of Environmental Treatment Techniques, 1(2): 69–75.
  18. Mohajan, H.K. (2013c), Singularity Theorems in General Relativity, M. Phil. Dissertation, Lambert Academic Publishing, Germany.
  19. Mohajan, H.K. (2015), Basic Concepts of Differential Geometry and Fibre Bundles, ABC Journal of Advanced Research, 4(1): 57–73.
  20. Penrose, R. (1972), Techniques of Differential Topology in Relativity, A.M.S. Colloquium Publications, SIAM, Philadelphia.
  21. Sachs, R.K. and Wu, H. (1977), General Relativity and Cosmology, Bulletin of the American Mathematical Society, 83(6): 1101–1164.
  22. Sánchez, M. (2010), Recent Progress on the Notion of Global Hyperbolicity, arXiv:0712.1933v2 [gr-qc] 25 Feb 2010.
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