NON-STATIONARY ROTATING BLACK HOLES: ENTROPY AND HAWKING'S RADIATION

In this paper we derive a class of non-stationary rotating solutions including Vaidya–Bonnor–de Sitter, Vaidya–Bonnor-monopole and Vaidya–Bonnor–Kerr. The rotating Viadya–Bonnor–de Sitter solution describes an embedded black hole that the rotating Vaidya–Bonnor black hole is embedded into the rotating de Sitter cosmological universe. In the case of the Vaidya–Bonnor–Kerr, the rotating Vaidya–Bonnor solution is embedded into the vacuum Kerr solution, and similarly, Vaidya–Bonnor-monopole. By considering the charge to be function of u and r, we discuss the Hawking's evaporation of the masses of variable-charged non-embedded, non-rotating and rotating Vaidya–Bonnor, and embedded rotating, Vaidya–Bonnor–de Sitter, Vaidya–Bonnor-monopole and Vaidya–Bonnor–Kerr, black holes. It is found that every electrical radiation of variable-charged black holes will produce a change in the mass of the body without affecting the Maxwell scalar in non-embedded cases; whereas in embedded cases, the Maxwell scalar, the cosmological constant, monopole charge and the Kerr mass are not affected by the radiation process. It was also found that during the Hawking's radiation process, after the complete evaporation of masses of these variable-charged black holes, the electrical radiation will continue creating (i) negative mass naked singularities in non-embedded ones, and (ii) embedded negative mass naked singularities in embedded black holes. The surface gravity, entropy and angular velocity of the horizon are presented for each of these non-stationary black holes.