Considering the relationship between the black hole horizon and the cosmological horizon, the thermodynamic property of the charged de Sitter spacetime is discussed. The effective temperature and energy are obtained. The result shows that the upper limit of the energy in the charged de Sitter spacetime is just the energy in the pure de Sitter spacetime. The thermal capacity of the charged de Sitter spacetime is positive, thus satisfying the thermal stability condition.
Using the Unruh-Verlinde temperature obtained by the idea of entropy force,we directly calculated the partition functions of Boson field in Reissner-Nordstro¨m spacetime with quantum statistical method.We obtain the expression of the black hole quantum statistical entropy.We find that the term is proportional to the area of black hole horizon and the logarithmic correction term appears.Our result is valid for flat spacetime.
We study the Hawking radiation of the scalar field in the rotating Gdel black hole in minimal five-dimensional supergravity. We not only derive radiation spectra that satisfy the unitary principle but also obtain the correction term of Bekenstein-Hawking entropy. The conclusion will help us learn more about the rotating Gdel black hole in minimal five-dimensional supergravity. This provides a greater understanding of the thermal radiation of black holes.
