Bigravity black hole and its thermodynamics

Abstract

We argue that the Isham-Storey exact solution to bigravity does not describe black holes because the horizon is a singular surface. However, this is not a generic property of bigravity, but a property of a particular potential. More general potentials do accept regular black holes. For regular black holes, we compute the total energy and thermodynamical parameters. Phase transitions occur for certain critical temperatures. We also find a novel region on phase space describing up to 4 allowed states for a given temperature.

On horizon structure of bimetric spacetimes

“…In the spherically symmetric case, the result of proposition 3 was proved in Ref. [17] using coordinate-based arguments.…”

“…[17], where it was argued that the presence of the g µν horizon implies that the 1-form dt is singular at r H , so that f µν will be singular at r H unless J(r H ) = 0. As discussed below, this reasoning is not conclusive, because at r H the 1-form dr becomes proportional to dt, so a diverging coefficient of dr 2 could potentially cancel the singularity and render the geometry regular.…”

On AdS to dS transitions in higher-curvature gravity

“…This behavior corresponds to a zeroth-order phase transition, a not very common feature in physical systems, but already described in other circumstances. See, for example [35,36] for zerothorder transitions in the context of self-gravitating gases, and [33,37,38] in the context of black hole thermodynamics.…”

Asymptotically flat spacetimes in 3D bigravity

“…There are much literature and recent work on this theory (see [11] for the original paper). For recent reviews and new results, including black holes properties, cosmological implications and its relation with massive gravity, see [12][13][14][15][16] and references there in and there off.…”