Mining metrics for buried treasure

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.

16 pages, no figures, minor grammatical changes, submitted to Proceedings of the Malcolm@60 Conference (London, July 2004)

References in corpus (4)

• Axial symmetry and conformal Killing vectors
• On the interpretation of cylindrically symmetric Levi-Civita spacetime for 0<sigma<infinity
• Quantum singularity of Levi-Civita spacetimes
• Classical and Quantum Singularities of Levi-Civita Spacetimes with and without a Positive Cosmological Constant

Cited by in corpus (9)

• Cylindrically Symmetric Relativistic Fluids: A Study Based on Structure Scalars
• Shearfree Cylindrical Gravitational Collapse
• Stationary Cylindrical Anisotropic Fluid
• Quantum healing of classical singularities in power-law spacetimes
• Quantum singularities in static and conformally static space-times
• Quantum singularities in spherically symmetric, conformally static spacetimes
• Semiclassical backreaction around a nearly spinning cosmic string
• Classical and quantum properties of a 2-sphere singularity
• Report on workshop A1: Exact solutions and their interpretation