Vaidya Solution in Non-Stationary de Sitter Background: Hawking’s Temperature

ABSTRACT

In this paper we propose a class of non-stationary
solutions of Einstein’s field equations describing an embedded Vaidya-de Sitter
solution with a cosmological variable function Λ(*u*). Vaidya-de Sitter
solution is interpreted as the radiating Vaidya black hole which is embedded
into the non-stationary de Sitter space with variable Λ(*u*). The energymomentum
tensor of the Vaidya-de Sitter black hole may be expressed as the sum of the
energy-momentum tensor of the Vaidya null fluid and that of the non-stationary
de Sitter field, and satisfies the energy conservation law. We also find that
the equation of state parameter *w*= *p/ρ *= *-*1 of the
non-stationary de Sitter solution holds true in the embedded Vaidya-de Sitter
solution. It is also found that the space-time geometry of non-stationary
Vaidya-de Sitter solution with variable Λ(*u*) is type D in the Petrov
classification of space-times. The surface gravity, temperature and entropy
of the space-time on the cosmological black hole horizon are discussed.

Cite this paper

N. Ishwarchandra and K. Singh, "Vaidya Solution in Non-Stationary de Sitter Background: Hawking’s Temperature,"*International Journal of Astronomy and Astrophysics*, Vol. 3 No. 4, 2013, pp. 494-499. doi: 10.4236/ijaa.2013.34057.

N. Ishwarchandra and K. Singh, "Vaidya Solution in Non-Stationary de Sitter Background: Hawking’s Temperature,"

References

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[13] A. Wang and Y. Wu, “LETTER: Generalized Vaidya Solutions,” General Relativity and Gravitation Vol. 31, No. 1, 1999, pp. 107-114. http://dx.doi.org/10.1023/A:1018819521971

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[15] A. H. Guth, “Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems,” Physical Review D, Vol. 33, No. 2, 1981, pp. 347-356. http://dx.doi.org/10.1103/PhysRevD.23.347

[16] B. Carter, “Black Hole Equilibrium States,” In: C. deWitt and B. deWitt, Eds., Black Holes, Gordon and Breach Science Publishers, New York, 1973, pp. 57-214.

[17] J. W. York, “What Happens to the Horizon When a Black Hole Radiates,” In: S. M. Christensen, Ed., Quantum Theory of Gravity: Essays in Honor of the 60th Birthday of Bryce S. De-Witt, Adam Hilger, Bristol, 1984, pp. 136-147.

[1] P. C. Vaidya, “The External Field of a Radiating Star in General Relativity,” Current Science, Vol. 12, 1943, pp. 183-184; reprinted General Relativity and Gravitation, Vol. 31, No. 1, 1999, pp. 119-120. http://dx.doi.org/10.1023/A:1018871522880

[2] G. W. Gibbons and S. W. Hawking, “Cosmological Event Horizons, Thermodynamics, and Particle Creation,” Physical Review D, Vol. 15, No. 10, 1977, pp. 2738-2751. http://dx.doi.org/10.1103/ PhysRevD.15.2738

[3] R. G. Cai, J. Y. Ji and K. S. Soh, “Action and Entropy of Black Holes in Spacetimes with a Cosmological Constant,” Classical and Quantum Gravity, Vol. 15, No. 9, 1998, pp. 2783-2793. http://dx.doi.org/10. 1088/0264-9381/15/9/023

[4] R. L. Mallett, “Radiating Vaidya Metric Embedded in de Sitter Space,” Physical Review D, Vol. 31, No. 2, 1985, pp. 416-417. http://dx.doi.org/10.1103/PhysRevD.31.416

[5] R. L. Mallett, “Evolution of Evaporating Black Holes in an Inflationary Universe,” Physical Review D, Vol. 33, No. 8, 1986, pp. 2201-2204. http://dx.doi.org/10.1103/PhysRevD.33.2201

[6] N. Ibohal, “Non-Stationary de Sitter Cosmological Models,” International Journal of Modern Physics D, Vol. 18, No. 5, 2009, pp. 853-863. http://dx.doi.org/10.1142/S0218271809014807

[7] S. W. Hawking and G. F. R. Ellis, “The Large Scale Structure of Space-Time,” Cambridge University Press, Cambridge, 1973.

[8] E. T. Newman and R. Penrose, “An Approach to Gravitational Radiation by a Method of Spin Coefficients,” Journal of Mathematical Physics, Vol. 3, No. 3, 1962, pp. 566-578. http://dx.doi.org/10. 1063/1.1724257

[9] T. Padmanabhan, “Cosmological Constant—The Weight of the Vacuum,” Physics Reports, Vol. 380, No. 5-6, 2003, pp. 235-320. http://dx.doi.org/10.1016/S0370-1573(03)00120-0

[10] E. J. Copeland, M. Sami and S. Tsujikawa, “Dynamics of Dark Energy,” International Journal of Modern Physics D, Vol. 15, No. 11, 2006, pp. 1753-1935. http://dx.doi.org/10.1142/S021827180600942X

[11] R. Bousso, “The Cosmological Constant,” General Relativity and Gravitation, Vol. 40, No. 2, 2008, pp. 607-637. http://dx.doi.org/10.1007/s10714-007-0557-5

[12] N. Ibohal, “On the Variable-Charged Black Holes Embedded into de Sitter Space: Hawking’s Radiation,” International Journal of Modern Physics D, Vol. 14, No. 6, 2005, pp. 973-994.

[13] A. Wang and Y. Wu, “LETTER: Generalized Vaidya Solutions,” General Relativity and Gravitation Vol. 31, No. 1, 1999, pp. 107-114. http://dx.doi.org/10.1023/A:1018819521971

[14] S. Chandrasekhar, “The Mathematical Theory of Black Holes,” Clarendon Press, Oxford, 1983.

[15] A. H. Guth, “Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems,” Physical Review D, Vol. 33, No. 2, 1981, pp. 347-356. http://dx.doi.org/10.1103/PhysRevD.23.347

[16] B. Carter, “Black Hole Equilibrium States,” In: C. deWitt and B. deWitt, Eds., Black Holes, Gordon and Breach Science Publishers, New York, 1973, pp. 57-214.

[17] J. W. York, “What Happens to the Horizon When a Black Hole Radiates,” In: S. M. Christensen, Ed., Quantum Theory of Gravity: Essays in Honor of the 60th Birthday of Bryce S. De-Witt, Adam Hilger, Bristol, 1984, pp. 136-147.