Thermal phase transition in F(R) -charged AdS4 scalar theory

Abstract

We investigate instabilities of $F(R)$-charged ${\mathrm{AdS}}_{4}$ black holes by a massive charged scalar field in a linear perturbation regime. We study tachyonic instabilities as the near horizon scalar condensation in a model of $F(R)$ gravity with planar horizon and investigate properties of possible phase transitions. The results show that such transitions are sensitive to the first derivative of $F(R)$ with respect to $R$ in that the larger its value, the higher the critical temperature, thus resulting in a new generation of high-temperature superconductors. Also, for a certain range of parameters, $F(R)$-charged ${\mathrm{AdS}}_{4}$ black holes suffer from superradiant instability. We consider the effects of the scalar mass and charge on such instabilities and conclude that Reissner-Nordstrom (RN) black holes decay into small hairy black holes that have a charged scalar condensate floating near the horizon. It is shown that the existence of phase transition at the critical temperature leading to a hairy black hole solution emerges for $T<{T}_{c}$, while RN black holes exist for $T>{T}_{c}$. The effect of $F(R)$ on the critical temperature is subsequently investigated in the case of superradiant instability, showing that higher critical temperatures would be possible in $F(R)$ gravity. We also check the stability of hairy black holes and show that the resulting hairy solution can be considered as a possible endpoint of superradiant instability of a small charged black hole.