Quantum Singularities in Spherically Symmetric Black Hole Spacetimes

Classical general relativity predicts the existence of irremovable singularities, indicated by incomplete geodesic paths in spacetime. These singularities are prevalent in a host of relativistic spacetimes, including those of observable cosmological objects such as various black hole systems. However, by analyzing a quantum wave packet instead of geodesic incompleteness, the potential exists to ``remove'' or ``heal'' these singularities. In this case, no boundary conditions are needed to be put on the singularity. Our technique focuses on analysis of the spatial segment of the uncoupled, relativistic Klein Gordon wave operator for a massless scalar particle and determining if it is essentially self-adjoint. In particular, Weyl's limit point - limit circle criterion are used to determine self-adjointness. Through self-adjointness properties, the spacetime can be characterized as quantum mechanically singular or non-singular. In our study, timelike curvature singularities associated with a group of spherically symmetric spacetimes are analyzed. Our results indicate the wave operator is not essentially self-adjoint for these spacetimes. Hence, they contain quantum singularities.