Instability of flat space for massive gravitational fields.

Abstract

Flat space is not stable in massive gravity, in the sense that for any nonzero graviton mass m, no matter how small it may be, any nontrivial solution for the massive field equations is not asymptotically flat as one goes far away from the source, i.e., r\ensuremath{\rightarrow}\ensuremath{\infty}. This is because, although one may be able to construct a locally stable solution with respect to flat space, it does not approach flat space in the limit r\ensuremath{\rightarrow}\ensuremath{\infty}. This is still true even if one takes a successive set of both limits r\ensuremath{\rightarrow}\ensuremath{\infty} and m\ensuremath{\rightarrow}0. Flat space in massive gravity as well as in its massless limit is only an isolated trivial solution. This leads to the conclusion that Einstein's general relativity is an isolated theory.