Higher-dimensional black holes in massive gravity charged with a conformal-invariant field

Abstract

Making use of a model of nonlinear electrodynamics (NED), whose action remains invariant under conformal transformations, a new class of charged higher-dimensional black holes (BHs) has been introduced in the massive gravity theory. Our exact solutions, with A(dS) asymptotic behavior, in addition to the BHs with one, two and three horizons, show the extreme and horizon-less ones. The conserved and thermodynamic quantities have been calculated in the presence of massive gravitons and NED. By use of a Smarr mass formula, it has been found that the standard form of the first law of BH thermodynamics (FLT) remains valid for our new massive BHs. Thermal stability of the BHs has been studied comparatively, by use of the geometrical and thermodynamical methods. The size of those BHs which undergo first- or second-order phase transition, as well as those of which are locally stable has been determined. The results of geometrical and thermodynamical approaches have been compared, for bout of dS and AdS cases, by use of the plots. It has been shown that both of the aforementioned methods produce the same results provided that HPEM or Quevedo type-two (QII) metrics are used. Critical behavior of the BHs has been studied by taking thermodynamic pressure proportional to the cosmological constant. It has been found that in addition to the Van der Waals (VdW) like phase transition, the so-called reentrant phase transition (RPT) can occur as well.