Instability of BTZ black holes in parity-even massive gravity

Abstract

We investigate the linearized equations of motion in three dimensional Born-Infeld gravity theory. Motivated by this model, we calculate the quasinormal modes of BTZ black hole solutions of parity-even gravity theories in three dimensions by using numerical methods. The results are classified in three families and they are so accurate such that it allows us to propose analytical form for the quasinormal frequencies. We find new quasinormal modes which have been missing in the literature of the analytical studies of three dimensional massive gravitons. These new modes do not have the known tower structure and they are purely imaginary for any value of the angular momenta. Considering the complete set of the quasinormal modes, we show that the BTZ black hole solutions are unstable for any value of the parameters of the theory. We confirm our numerical results by computing the new eigenmodes analytically at zero angular momentum.

Five-Dimensional Yang-Mills Black Holes in Massive Gravity's Rainbow

“…In fact, the reentrant phase transitions for an AdS black hole solution has also been studied using this formalism [50][51][52]. It is interesting to analyze critical behavior for black hole solutions in massive gravity, and the graviton mass can produce new non-trivial phase transitions [53,54].…”