Quantum singularities in self-similar spacetimes

Singularities, which are commonplace in general relativity, are indicated by causal geodesic incompleteness in otherwise maximal spacetimes. Can such singularities be healed (or resolved) quantum mechanically? Geodesics are in effect the paths of classical particles, which led Horowitz and Marolf to propose that they be replaced by quantum wave packets. Then a singularity is healed if the quantum wave operator can be shown to be essentially self-adjoint. We explore here a generalized Horowitz-Marolf approach for conformally static spacetimes in the context of the Klein-Gordon operator in the vicinity of singularities in the self-similar spacetimes introduced by Brady. We show that it fails the self-adjointness test for an entire generic class of spacetimes that have asymptotically power-law metric coefficients near the classically-singular origin, so the singularities in these spacetimes cannot be healed using quantum wave packets.