On metric-connection compatibility and the signature change of space-time
arXiv:gr-qc/9802058 · doi:10.1238/Physica.Regular.066a00401
Abstract
We discuss and investigate the problem of existence of metric-compatible linear connections for a given space-time metric which is, generally, assumed to be semi-pseudo-Riemannian. We prove that under sufficiently general conditions such connections exist iff the rank and signature of the metric are constant. On this base we analyze possible changes of the space-time signature.
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