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 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.
