MG12 - Talk detail
 

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Abstract

Quantum Particle Behavior in Classically Singular Space-times

A small step towards understanding the presence of singularities in a fully quantum universe is the study of singularities in the presence of quantum fields. In this presentation I will discuss space-times which can be thought of as classically singular but are not quantum mechanically singular in that the spatial portion of the quantum wave operator is not essentially self-adjoint. Spacetimes with all three classes of classical singularity, i.e. scalar curvature, non-scalar curvature and quasi-regular, will be tested. In particular, certain space-times which obey the standard energy conditions but contain strong singularities will be shown to be quantum mechanically non-singular.

Singularity Structure of Space-times with Higher-Order Diverging Differential Curvature Invariants

The classical singularity structure of general relativistic space-times is determined by incomplete geodesics and the divergence of scalar polynomials in the curvature. The quantum singularity structure is determined by the essential self-adjointness of scalar wave operators evaluated for test fields in the space-times. Here we discuss a class of space-times with only a higher-order divergence in the scalar polynomials, a class first discussed by P. Musgrave and K. Lake (Class. Quantum Grav. 12 (1995) L39-L41). We show that these spherically symmetric static space-times, which can be in some sense considered classically singular, are unambiguously quantum mechanically non-singular. We hope to shed some light on these highly unusual space-times.

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