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Mining metrics for buried treasure. (English) Zbl 1145.83342
Summary: The same but different: That might describe two metrics. On the surface CLASSI may show two metrics are locally equivalent, but buried beneath may be a wealth of further structure. This was beautifully described in a paper by Malcolm MacCallum in [Gen. Relativ. Gravitation 30, No. 1, 131–150 (1998; Zbl 0926.53043)]. 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 K. P. Tod in [Classical Quantum Gravity 11, No. 5, 1331–1339 (1994; Zbl 0798.53081)]) 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.

MSC:
83C75 Space-time singularities, cosmic censorship, etc.
83C20 Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory
83C15 Exact solutions to problems in general relativity and gravitational theory
Software:
SHEEP
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References:
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