Abstract
It is stated in many text books that the any metric appearing in general relativity should be locally Lorentzian i.e. of the type η μ ν =diag (1,−1,−1,−1) this is usually presented as an independent axiom of the theory, which can not be deduced from other assumptions. The meaning of this assertion is that a specific coordinate (the temporal coordinate) is given a unique significance with respect to the other spatial coordinates. In this work it is shown that the above assertion is a consequence of requirement that the metric of empty space should be linearly stable and need not be assumed.
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Yahalom, A. The Geometrical Meaning of Time. Found Phys 38, 489–497 (2008). https://doi.org/10.1007/s10701-008-9215-3
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DOI: https://doi.org/10.1007/s10701-008-9215-3