Abstract
The problem of whether or not two different mathematical models of space-time describe the same space-time is not trivial. For example, the first spherically symmetric solution—the Schwarzschild metric—describes only part of the process of falling into a black hole, and other metrics were discovered for the same situation that also describe the subsequent events. These metrics turned out to be isomorphic in the sense that some 1-1 correspondence (coordinates transformations) transform one into another. But in the general case to find whether such an isomorphism exists is a difficult computational problem. There are some algorithms for smooth metrics, but the problem is also important for the nonsmooth metrics involving singularities. We prove that in the general case this isomorphism problem is intractable.
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Kreinovich, V. Space-time isomorphism problem is intractable (NP-hard). Int J Theor Phys 30, 1249–1257 (1991). https://doi.org/10.1007/BF00671011
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DOI: https://doi.org/10.1007/BF00671011