On the instability of ultracompact horizonless spacetimes

Understand

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.