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 fi nd 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 classi fi cation of space-times. The surface gravity, temperature and entropy of the space-time on the cosmological black hole horizon are discussed.