Thermodynamic Phase Transition of Anti De Sitter Schwarzschild Scalar-Tensor-Vector-Black Holes

Document Type : Research Paper


1 Faculty of Physics, Semnan Universiy, Semnan, Iran, 35131-19111

2 Faculty of physics, Semnan University


Instead ofscalar-tensor gravity

models which are applicable for

description of cosmic inflation with unknown dark sector of

matter/energy, at present tense

there are presented different alternative

scalar-tensor-vector gravities

where meaningful dynamical vector fields can support cosmic

inflation well without to use dark matter/energy concept. One of

these gravity models was presented by Moffat which

its modified Schwarzschild black hole solution is used to

study thermodynamic phase transition in presence of the AdS space

pressure in this article. To do

so, we obtained an equation of state which asymptotically reaches

to equation of state of ideal gas for large black holes but for

small scale black holes we obtained a critical point at phase

space where the black hole can be

exhibited with a phase transition

at processes ofisothermal and

isobaric. By looking at diagrams of the Gibbs free energy and the

heat capacity at constant pressure which are plotted versus the

temperature and the specific volume one can see an inflection

point which means that the phase transition is

second order type. In fact there

is small to large phase transition for the black hole which is

equivalent to the Van der Waals liquid-gas phase transition in

ordinary thermodynamic systems. The phase transition

happens below the critical point

in phase space when the gravitational charge of the black hole is

equal to its mass.