Spherically symmetric analysis on open FLRW solution in non-linear
  massive gravity
  We study non-linear massive gravity in the spherically symmetric context. Our
main motivation is to investigate the effect of helicity-0 mode which remains
elusive after analysis of cosmological perturbation around an open
Friedmann-Lemaitre-Robertson-Walker (FLRW) universe. The non-linear form of the
effective energy-momentum tensor stemming from the mass term is derived for the
spherically symmetric case. Only in the special case where the area of the two
sphere is not deviated away from the FLRW universe, the effective energy
momentum tensor becomes completely the same as that of cosmological constant.
This opens a window for discriminating the non-linear massive gravity from
general relativity (GR). Indeed, by further solving these spherically symmetric
gravitational equations of motion in vacuum to the linear order, we obtain a
solution which has an arbitrary time-dependent parameter. In GR, this parameter
is a constant and corresponds to the mass of a star. Our result means that
Birkhoff's theorem no longer holds in the non-linear massive gravity and
suggests that energy can probably be emitted superluminously (with infinite
speed) on the self-accelerating background by the helicity-0 mode, which could
be a potential plague of this theory.
