The Relation between the Quasi-Localized Energy-Momentum Complexes and the Thermodynamic Potential for the Schwarzschild-de Sitter Black Hole

The Schwarzschild-de Sitter black hole solution, which has two event horizons, is considered to examine the relation between the energy component of quasi-localized energy-momentum complexes on M and the heat flows passing through its boundary ∂M. Here M is the patch between cosmological event horizon and black hole event horizon of the SdS black hole solution. Conclusively, the relation, like the Legendre transformation, between the energy component of quasi-localized Einstein and Møller energy-momentum complex and the heat flows passing through the boundary is obeyed, and these two energy components of quasi-localized energy-momentum complexes could be corresponding to thermodynamic potentials.

Thermodynamic properties of black holes in de Sitter space

We study the thermodynamic properties of Schwarzschild–de Sitter (SdS) black hole and Reissner–Nordström–de Sitter (RNdS) black hole in view of global and effective thermodynamic quantities. Making use of the effective first law of thermodynamics, we can derive the effective thermodynamic quantities of de Sitter black holes. It is found that these effective thermodynamic quantities also satisfy Smarr-like formula. Especially, the effective temperatures are nonzero in the Nariai limit. By calculating heat capacity and Gibbs free energy, we find SdS black hole is always thermodynamically stable and RNdS black hole may undergoes phase transition at some points.

Low energy greybody factors for fermions emitted by a Schwarzschild-de Sitter black hole

In this paper, we are discussing the problem of low energy greybody factors for fermions emitted by a Schwarzschild-de Sitter (SdS) black hole. In our study, we are using the analytical methods proposed by Unruh some time ago for determining the greybody factors. We have found that at low energies the greybody factors are constant for a given total angular momentum (similar to what happens in the case of scalar particles reported before in the literature). Also, our results are indicating an enhancement in the energy spectrum if one is increasing the value of the cosmological constant. These results are consistent with numerical calculations performed by S. F. Wu et al., Phys. Rev. D 78 (1998) 084010.

EFFECT OF COSMIC STRING IN SPHERICALLY SYMMETRIC BLACK HOLE ON THE DIRAC PERTURBATION

The effect of cosmic string on the quasinormal modes (QNMs) of massless Dirac field perturbations were studied in different black hole spacetimes. Quasi-normal mode frequencies of massless Dirac field in Schwarzschild, RN extremal, SdS and near extremal SdS black hole spacetimes with cosmic string are obtained using WKB approximation. Our study shows a clear deviation in QNMs due to presence of cosmic string from those in the absence of string. The influence of cosmic string coded in the form of an increase in the oscillation frequency and damping time of QNMs.

ABSORPTION CROSS-SECTION OF A SCHWARZSCHILD–DE SITTER BLACK HOLE

The Hawking temperature corresponding to the black hole horizon of Schwarzschild–de Sitter (SdS) black hole was found using WKB approximation and the effect of reflection of waves from the quantum horizon. The absorption cross-section σ abs when SdS black hole is placed in a Klein-Gordon field is calculated and is found to be inversely proportional to the Hawking temperature.

Logarithmic Corrections to the FRW Brane Cosmology from 5d Schwarzschild–de Sitter Black Hole

Thermodynamics of 5d SdS black hole is considered. Thermal fluctuations define the (sub-dominant) logarithmic corrections to black hole entropy and then to Cardy–Verlinde formula and to FRW brane cosmology. We demonstrate that logarithmic terms (which play the role of effective cosmological constant) change the behavior of 4d spherical brane in dS, SdS or Nariai bulk. In particularly, bounce Universe occurs or 4d dS brane expands to its maximum and then shrinks. The entropy bounds are also modified by next-to-leading terms. Out of braneworld context the logarithmic terms may suggest slight modification of standard FRW cosmology.