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

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 coupled the new model with a nondynamical curved background in [Phys. Rev. D 90, 123013 (2014)] and constructed new interaction terms without the 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 conditions 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 on the Einstein gravity by calculating the black hole entropy, since the gravity coupled with massive spin-two theory admits a black hole solution in addition to the (anti-)de Sitter space solution.

Figure 1

The parameter region for the constant curvature spacetime.