Speaker
Description
We construct the canonical ensemble of a matter thin shell in
asymptotically AdS using the Euclidean path integral approach.
We impose spherical symmetry, the Hamiltonian and momentum constraints,
the hot AdS regularity conditions and the asymptotic behaviour of AdS
on the metrics summed in the path integral and obtain the reduced action,
which can be regarded as a generalized free energy. We then perform
the zero loop approximation, i.e. the path integral is given solely by
the contribution of the stationary points of the action. We obtain the
equations of stationarity and stability in general, showing that
stability is guaranteed if the gravitational radius increases as temperature
increases and if the shell is mechanically stable. We show this system can
be described as a particular case of a system only dependent on the gravitational
radius although one looses the mechanical stability condition.
We use a specific equation of state for the shell and find five solutions for the shell,
with two solutions being stable: one with no shell, i.e. hot AdS; and one with a shell.
We obtain the thermodynamic quantities of the ensemble, the mean energy, the mean
pressure and the entropy, which in this case corresponds to the entropy of the shell.
The ensemble is thermodynamically stable if the heat capacity is positive, while the
mechanical stability cannot be described by thermodynamic variables of the system.
We compare the two stable solutions and the stable black hole solution of
Hawking and Page in the context of phase transitions and determine
the favorable solution for fixed temperatures, by analyzing which solution has
the lowest free energy.
