Quantum resolution of timelike singularities in static and conformally static spacetimes

Series: 
The London Relativity and Cosmology Seminar
Speaker: 
Debbie Konkowski (Naval Academy, Annapolis)
Date: 
May 8th, 2013 at 16:30
Room: 
Maths 103
Abstract: 

A proposal for resolving a singularity in a static spacetime with a timelike singularity using quantum fields originated with a paper by Horowitz and Marolf following pioneering work by Wald. A static spacetime is termed quantum mechanically non-singular if the spatial portion of the relevant wave operator is essentially self-adjoint on Co∞(Σ) in the space of square-integrable functions L2(Σ), where Σ is a spatial slice.

In this talk, after the usual definitions of classical and quantum singularities are reviewed, examples of quantum singularities in static space-times are given. These include asymptotically power-law space-times, space-times with diverging higher-order differential invariants, and a space-time with a 2-sphere singularity.

We follow this by showing that the Horowitz and Marolf definition of quantum non-singularity for static spacetimes can be extended to the case of conformally static spacetimes and test the formalism for a FRW cosmology with a cosmic string and for a class of conformally static, spherically symmetric spacetimes. We use as quantum fields the solutions of the generally coupled, massless Klein-Gordon equation, and Weyl's limit point - limit circle criteria for judging the existence of quantum singularities. This requires that we write the radial part of the Klein-Gordon equation in the form of a one-dimensional Schrödinger equation, and evaluate the behavior of the associated potential energy in the vicinity of the singularity. In this way we find the ranges of metric parameters and coupling coefficients for which classical timelike singularities in these spacetimes are resolved quantum mechanically.