Thermodynamics of Vaidya-Bonner-de Sitter space time based on the generalized space-time uncertainty

Abstract

In each static or stationary space time k is just surface gravity of the horizon, but in the of Vaidya-Bonnerde Sitter space time, it is no longer the surface gravity of the event horizon. This property makes the VaidyaBonner as an important horizon. In this paper, the entropy of Vaidya-Bonner-de Sitter space time is calculated. In continue, employing the generalized uncertainty principle, quantum gravitational corrections to the entropy of VaidyaBonner space time is studied.It is interesting that without calculating the energy-momentum tensor of evaporating black hole we calculate the temperature of its event horizon. The of Vaidya-Bonner-de Sitter calculation is the simple method that without calculating the vacuum expectation value of the renormalized energymomentum tensor, we can determine the horizon's temperature. In this scenario, the Klein-Gordon equation can be reduced to the standard form of wave equation in the tortoise coordinate of the Schwarzschild space time. However in a non-static space time Zheng-Dai approaches give the horizon's temperature. Recently this method have received much attention (Zheng and Xianxin 1992;Zheng et al. 1994;Damour and Ruffini 1976;Balbinot 1986;Hiscock 1981). On the other hand, some property of the Vaidya-Bonner space time differ it with other space times.A. Farmany ( ) Young Researchers Club, Hamedan Branch, Islamic Azad University, For example, in each static or stationary space time k is just the surface gravity of the horizon, but in the VaidyaBonner-de Sitter space time, it is no longer the surface gravity of event horizon and the cosmic horizon. This property makes the Vaidya-Bonner solution as an important horizon (Chen and Yang 2007;Liu et al. 2003;Li and Zhao 2001;Lin and Yang 2009;Zhou and Liu 2009;Li et al. 1999;Niu and Liu 2010). In this letter, we calculate the entropy of the Vaidya-Bonner-de Sitter space time. Let we begin with the Vaidya-Bonner-de Sitter solution,Where ς = 2m r + Q 2 r 2 + λr 2 3 and λ is the cosmological constant. Not that mass and charge are Eddington-Finkelstein time ν dependent. , Wanglin et al. (2007 the Hawking temperature of the Vaidya-Bonner-de Sitter event horizon is obtained from a solution to the surface gravity of this space time,The black hole entropy is usually derived from the Hawking temperature. Setting M to mean energy and T to mean temperature, the entropy may defined from the well-known thermodynamics relation as,Inserting (2) into (3), one find dM dS = r − m − 2 3 λr 2 − 2rṙ 2πK B ςr 2 (4)

Compact objects in conformal nonlinear electrodynamics

“…This fact allows to apply the features of Vaidya-Bonnor solution to it's CNED extension (5.6). For instance, to describe thermodynamics of the star one can fully use the results obtained in [37,38], so the Hawking temperature on the event or on the cosmic horizon r h reads as:…”

Surrounded Bonnor–Vaidya solution by cosmological fields

“…are special subclasses of this solution [18,58]. Some interesting features of these black holes can be found in [15,19,20,59]. • The solution by setting f = f (r ) and ρ s = ρ s (r )…”