Quantum Probes of Spacetime Singularities

TL;DR

The paper investigates whether timelike spacetime singularities are genuinely problematic when probed by quantum particles. It develops a static-spacetime framework where the evolution is governed by a spatial operator $A = -V D^i(VD_i) + V^2 m^2$ on a Hilbert space with measure $V^{-1}d\Sigma$, and quantum regularity is determined by the essential self-adjointness of $A$, yielding a unique evolution via $A_E$. It demonstrates concrete examples where quantum probes are well defined—such as extremal dilaton black holes with $1<a^2\le 3$ and the fundamental string solution—despite classical curvature singularities, and analyzes scattering to show unitary evolution for timelike singularities in highly symmetric cases. The work also outlines extensions to time-dependent backgrounds through a field-theoretic approach, and discusses implications for quantum gravity and string theory in the presence of singular spacetimes.

Abstract

It is shown that there are static spacetimes with timelike curvature singularities which appear completely nonsingular when probed with quantum test particles. Examples include extreme dilatonic black holes and the fundamental string solution. In these spacetimes, the dynamics of quantum particles is well defined and uniquely determined.