Classical stability of BTZ black holes in new massive gravity

Abstract

We study the stability of the BTZ black hole in the new massive gravity. This is a nontrivial task because the linearized equation around the BTZ black hole background is a fourth-order differential equation. Away from the critical point of m 2 ' 2 ¼ 1=2, this fourth-order equation is split into two secondorder equations: one describes a massless graviton, and the other is designed for a massive graviton, which could be obtained from the Fierz-Pauli action. In this case, calculating quasinormal modes leads to confirming the stability of the BTZ black hole. At the critical point, we derive two left-and rightlogarithmic quasinormal modes from the logarithmic conformal field theory. Finally, we identify two s massive modes propagating on the black hole background through the conventional black hole stability analysis.

Gregory-Laflamme instability of the BTZ black hole in new massive gravity

“…This parity-even gravity describes two modes of helicity þ2 and À2 [2 degrees of freedom (DOF)] of a massive graviton, but it has a drawback of serving as a unitary model of massive gravity only in three dimensions [15]. For m 2 > 1=2' 2 with m 2 the mass of the graviton, the three-dimensional BTZ black hole in the new massive gravity is shown to be stable against the s-mode metric perturbation [16] when using the positivity of the potential outside the horizon. To this direction, it was recently reported that the stability of the BTZ black hole was mainly determined by the asymptotes of black hole spacetime: the condition of the s-mode stability is consistent with the generalized Breitenlohner-Freedman (BF) bound (m 2 !…”

Massive charged BTZ black holes in asymptotically (a)dS spacetimes

“…In addition, some of their stabilities have been addressed in refs. [46,47]. As for other three dimensional massive gravities, one can regard topological massive gravity [48], supergravity extensions [49] and critical gravity [50] (for more details, see ref.…”

Quasinormal modes and hidden conformal symmetry in the Reissner–Nordström black hole

“…On the other hand, the spin-2 and spin-3 quasinormal modes and frequencies around the BTZ black hole were constructed by the purely operator approach without any approximation [6,7,8].…”