Abstract
What is the fate of a star after it has exhausted its nuclear fuel? It can no longer remain in equilibrium, and must undergo gravitational collapse. If the stsar is not too massive it may settle down to a white dwarf or a neutron star. However, if the star is more massive than a few solar masses, then we have to invoke the general theory of relativity to study its final state. This theory is valid up to the Planck length (10-33 cm), below which quantum effects becomes important. In the early seventies, it was shown that singularities develop as a result of gravitational collapse where quantities such as the energy density of the collapsing matter and the curvature of the spacetime diverge [1]. However, the singularity theorems only predict the existence of singularities, but do not give any information about their nature or causal structure, e.g., can such a singularity communicate with a distant observer in the universe.
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References
S. W. Hawking and G. F. R. Ellis, “The Large Scale Structure of Spacetime”, Cambridge University Press, Cambridge, 1973.
P. S. Joshi, “Global Aspects in Gravitation and Cosmology”, Cambridge U- niversity Press, Cambridge, 1993
C. J. S. Clarke, Class. Quantum Grav., 10, 1375, 1993
T. P. Singh, in “Classical and Quantum Aspects of Gravitation and Cosmology”, eds. G. Date and B. R. Iyer, Institute of Mathematical Sciences Report 117, 1996
T. P. Singh, gr-qc/9805066; P. S. Joshi, gr-qc/0006101; S Jhingan and G. Magli, gr-qc/9903103.
R. Penrose, Riv. del Nuovo Cim., 1, 252, 1969.
R. M. Wald, gr-qc/9710068.
see, for example, Joshi (Ref. 2).
D. Markovic, S. L. Shapiro, Phys. Rev., D 61, 084029, 2000.
Lake, K. gr-qc/0002044 (unpublished)
R. Cai, L. Qiao and Y. Zhang, Mod. Phys. Lett. A 12, 155, 1997.
J. P. S. Lemos, Phys. Rev. D 59, 044020, 1999.
S. M. Wagh, S. D. Maharaj, Gen. Rel. Grav., 31, 975, 1999.
S. G. Ghosh and A. Beesham, Phys. Rev. D, 61, 067502, 2000.
S. W. Hawking and R. Penrose, “The Nature of Space and Time”, Princeton University Press, Princeton, 1996.
P. C. Vaidya, Proc. Indian Acad. Sci., A33, 264, 1951
P. C. Vaidya Reprinted, Gen. Rel. Grav., 31, 119, 1999.
P. C. Vaidya, and K. B. Shah, Proc. Nat. Inst. Sci., 23, 534, 1957.
W. B. Bonnor and P. C. Vaidya, Gen. Rel. Grav., 1, 159, 1970.
K. Lake and T. Zannias, Phys. Rev. D 43, 1798, 1991.
A. Wang, and Y. Wu, Gen. Rel. Grav., 31, 107, 1999
A. Patino and H. Rago, Phys. Lett., A 121, 329, 1987.
A. Ori, Class. Quantum Grav., 8, 1559, 1991.
m α v was introduced by A. Papapetrou (see Ref 5 above) and subsequently used by many authors, e2 ∝ v2 has been examined by Lake and Zannias (see Ref 7 above).
A spherical symmetric space-time is self similar if gtt(ct,cr) = gtt(t,r) and grr(ct,cr) = 9rr(t,r) for every c > 0. A self similar spacetime is characterized by the existence of a homothetic Killing vector.
First we note that eq. (16) being a cubic equation, it must have one real root. From theory of equation it is easy to see, for λ > 0 and µ2 > 0, any real root of the eq. (16) must be positive as negative values of Xo do not solve this equation.
S. S. Deshingkar, P. S. Joshi and I. H. Dwivedi, Phys. Rev., D 59, 044018, 1999.
B. C. Nolan, Phys. Rev. D, 60, 024014, 1999.
F. J. Tipler, C. J. S. Clarke, and G. F. R. Ellis, in “General Relativity and Gravitation”, ed. A. Held, Plenum, New York, 1980.
S. Barve and T. P. Singh, Mod. Phys. Lett., A12, 2415, 1997.
S. L. Shapiro and S. A. Teukolsky, Phys. Rev. Lett., 66, 994, 1991
ibid. Phys. Rev., D45 2006, 1992
P. S. Joshi and A. Krolak, Class. Quantum Grav., 13 3069, 1996
T. Nakamura, M. Shibata and K. Nakao, Prog. Theor. Phys., 89 821, 1993.
D. Christodoulou, Ann. Math., 140, 607, 1994;
D. Christodoulou, Ann. Math.149, 183, 1999.
M. W. Choptuik, Phys. Rev. Lett., 70, 9, 1993
C. Gundlack,gr-qc/0001046.
H. Iguchi, K. Nakao and T. Harada, Phys. Rev., D57, 7262, 1998
H. Iguchi, K. Nakao and T. Harada Prog. Thoer. Phys., 101, 1235, 1999.
R. V. Saraykar and S. H. Ghate, Class. Quantum Grav., 16, 281, 1999.
F. Mena, R. K. Tavakol and P. S. Joshi, gr-qc/0002062.
S. Hod and T. Piran, gr-qc/0011003.
A. Krilak, Prog. Theor. Phys. Suppl., 136, 45, 1999.
P. S. Joshi, N. Dadhich and R. Maartens, Mod. Phys. Lett. A, 15, 991, 2000
S. K. Chakravarti and P. S. Joshi, Int. J. Mod. Phys. D., 3, 647, 1994.
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Beesham, A., Ghosh, S.G. (2001). Gravitational Collapse. In: Sidharth, B.G., Altaisky, M.V. (eds) Frontiers of Fundamental Physics 4. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-1339-1_15
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