Unitarity and singular backgrounds

Understand

We compute the graviton Kaluza-Klein spectrum on a gravity-dilaton background with a naked singularity for all possible boundary conditions at the singularity which are consistent with unitary evolution.

• We apply methods from non-relativistic quantum mechanics with singular Schr\"{o}dinger potentials.
• In general the spectrum contains a tachyon, a sign of instability.
• Only for a particular boundary condition at the singularity is the spectrum free of tachyons.