Mining metrics for buried treasure

TL;DR

This paper explores how different metrics can reveal hidden structures and singularities in spacetime, using classical and quantum analyses to uncover deeper insights into exact solutions in general relativity.

Contribution

It demonstrates how quantum considerations can reveal hidden structures in spacetime metrics and deepen understanding of classical singularities and parameters.

Findings

Revealed hidden classical singularity structures in specific spacetime metrics

Showed quantum analysis can illuminate classical metric parameters

Compared Minkowski and Gal'tsov-Letelier-Tod spacetimes for structural insights

Abstract

The same but different: That might describe two metrics. On the surface CLASSI may show two metrics are locally equivalent, but buried beneath one may be a wealth of further structure. This was beautifully described in a paper by M.A.H. MacCallum in 1998. Here I will illustrate the effect with two flat metrics -- one describing ordinary Minkowski spacetime and the other describing a three-parameter family of Gal'tsov-Letelier-Tod spacetimes. I will dig out the beautiful hidden classical singularity structure of the latter (a structure first noticed by Tod in 1994) and then show how quantum considerations can illuminate the riches. I will then discuss how quantum structure can help us understand classical singularities and metric parameters in a variety of exact solutions mined from the Exact Solutions book.