Stability analysis for new theories of massive spin-two particle and black hole entropy of new bigravity

TL;DR

This paper analyzes the stability of a new ghost-free massive spin-two particle theory, explores its vacua in flat and curved spacetimes, and examines its impact on black hole entropy within a modified gravity framework.

Contribution

It introduces stability conditions for the new massive spin-two model in various spacetimes and investigates its implications for black hole entropy in bigravity theories.

Findings

Stable vacua conditions are established for flat and curved spacetimes.

The model admits black hole solutions affecting entropy calculations.

Nonlinear potential terms lead to nontrivial vacua without extra modes.

Abstract

In Phys.\ Rev.\ D 90 043006 (2014), we proposed a new ghost-free massive spin-two model in flat spacetime. Furthermore, as some extension, we couple the new model with a non-dynamical curved background in Phys.\ Rev.\ D 90 123013 (2014) and constructed new interaction terms without appearance of an extra mode. The characteristic property of the new model is the existence of nonlinear potential terms which give the nontrivial vacua. The presence of the nontrivial vacua, however, does not mean that the particle can be defined around all vacua. Therefore, in this paper, we discuss the condition for the new model to have stable vacua in flat spacetime and curved spacetime. Then, we couple this spin-two theory with a dynamical background and obtain the solutions. Moreover, we investigate the effect of this new spin-two model to the Einstein gravity by calculating the black hole entropy since the gravity coupled massive spin-two theory admits a black hole solution in addition to (anti-) de Sitter space solution.