Rotating embedded black holes: Entropy and Hawking's radiation

Abstract

In this paper, by applying Newman-Janis algorithm to a spherically symmetric ‘seed’ metric, we present general rotating metrics in terms of Newman-Penrose (NP) quantities involving Wang-Wu func- tions. From these NP quantities we present a class of rotating solutions including (i) Vaidya-Bonnor, (ii) Kerr-Newman-Vaidya, (iii) de Sitter, (iv) Kerr-Newman-Vaidya-de Sitter and (v) Kerr-Newman- monopole. The rotating Kerr-Newman-Vaidya solution represents a black hole that the Kerr-Newman black hole is embedded into the rotating Vaidya radiating universe. In the case of Kerr-Newman-Vaidya- de Sitter solution, one can describe it as the Kerr-Newman black hole is embedded into the rotating Vaidya-de Sitter universe, and similarly, Kerr-Newman-monopole. We have also discussed the physical properties by observing the energy momentum tensors of these solutions. These embedded solutions can be expressed in Kerr-Schild forms describing the extensions of Glass and Krisch superposition, which is further the extension of Xanthopoulos superposition. It is shown that, by considering the charge to be a function of radial coordinate, the Hawking’s continuous radiation of black holes can be expressed in classical spacetime metrics for these embedded black holes. It is also found that the electrical radiation will continue to form ‘instantaneous’ charged black holes and creating embedded negative mass naked singularities describing the possible life style of radiating embedded black holes during their contineous radiation processes. The surface gravity, entropy and angular velocity, which are important parameters of a horizon, are also presented for each of the embedded black holes.