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Mining metrics for buried treasure

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Abstract

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 1998. Here I will illustrate the effect with two flat metrics — one describing ordinary Minkowski spacetime and the other describing a threeparameter 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.

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Authors and Affiliations

  1. Department of Mathematics, U.S. Naval Academy, Maryland, Annapolis, 21402, USA

    D. A. Konkowski

  2. Department of Physics, Harvey Mudd College, California, Claremont, 91711, USA

    T. M. Helliwell

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  1. D. A. Konkowski
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  2. T. M. Helliwell
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Correspondence to D. A. Konkowski.

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Konkowski, D., Helliwell, T. Mining metrics for buried treasure. Gen Relativ Gravit 38, 1069–1082 (2006). https://doi.org/10.1007/s10714-006-0289-y

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