thermodynamic phase transition of anti de sitter schwarzschild scalar-tensor-vector-black holes

Instead ofscalar-tensor gravitymodels which are applicable fordescription of cosmic inflation with unknown dark sector ofmatter/energy, at present tensethere are presented different alternativescalar-tensor-vector gravitieswhere meaningful dynamical vector fields can support cosmicinflation well without to use dark matter/energy concept. one ofthese gravity models was presented by moffat whichits modified schwarzschild black hole solution is used tostudy thermodynamic phase transition in presence of the ads spacepressure in this article. to doso, we obtained an equation of state which asymptotically reachesto equation of state of ideal gas for large black holes but forsmall scale black holes we obtained a critical point at phasespace where the black hole can beexhibited with a phase transitionat processes ofisothermal andisobaric. by looking at diagrams of the gibbs free energy and theheat capacity at constant pressure which are plotted versus thetemperature and the specific volume one can see an inflectionpoint which means that the phase transition issecond order type. in fact thereis small to large phase transition for the black hole which isequivalent to the van der waals liquid-gas phase transition inordinary thermodynamic systems. the phase transitionhappens below the critical pointin phase space when the gravitational charge of the black hole isequal to its mass.