Speaker
Description
The grand canonical ensemble of a d-dimensional
Reissner-Nordström black hole space in a cavity is analyzed through
the Euclidean path integral approach. The partition function of the
ensemble is given in terms of the fixed temperature and fixed electric
potential at the boundary of the cavity. One performs the zero loop
approximation, i.e., only the contribution of the solutions which are
stationary points of the action are considered. One finds two
solutions for the charged black hole, 𝑟+1 and 𝑟+2, where
𝑟+2 is the largest. The stability is analyzed through
perturbations of the reduced action, yielding instability of 𝑟+1
and stability of 𝑟+2. Through the correspondence between the
partition function and the thermodynamic grand potential, one obtains
the mean energy, mean charge, the entropy and the thermodynamic
pressure of the system. Now, a spontaneous process in the grand
canonical ensemble can never increase the grand canonical potential
𝑊, otherwise the second law of thermodynamics would be violated.
Thus, it is of interest to compare, for a cavity with fixed size,
temperature, and electric potential, the value of 𝑊 for
the black hole 𝑟+2 solution with the value of 𝑊 of a
nongravitating charged shell, which serves as a model for charged hot
flat space. In this way, one can investigate possible phase
transitions between black holes and hot flat space.
