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General Relativity and Quantum Cosmology, gr-qc
Abstract:
Motivated by recent results reporting the instability of horizonless objects
with stable light rings, we revisit the linearized stability of such
structures. In particular, we consider an exterior Kerr spacetime truncated at
a surface where Dirichlet conditions on a massless scalar are imposed.This
spacetime has ergoregions and light rings when the surface is placed
sufficiently deep in the gravitational potential. We establish that the
spacetime is linearly, mode-unstable when it is sufficiently compact, in a
mechanism associated with the ergoregion. In particular, such instability has
associated zero-modes. At large multipole number the critical surface location
for zero modes to exist is precisely the location of the ergosurface along the
equator. We show that such modes don't exist when the surface is outside the
ergoregion, and that any putative linear instability mechanism acts on
timescales $\tau \gtrsim 10^5 M$, where $M$ is the black hole mass. Our results
indicate therefore that at least certain classes of objects are linearly stable
in the absence of ergoregions, even if rotation and light rings are present.
