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

Ngangbam Ishwarchandra, Kangujam Yugindro Singh

Department of Physics, Manipur University, Imphal, India.

DOI: 10.4236/ijaa.2013.34057                

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.

Keywords

Vaidya Solution; Non-Stationary de Sitter; Einstein’s Equations; Energy-Momentum Tensor

Conflicts of Interest

The authors declare no conflicts of interest.

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