Are the notions of past, present and future compatible with the General Theory of Relativity?

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The notions of time and causality are revisited, as well as the A- and B-theory of time, in order to determine which theory of time is most compatible with relativistic spacetimes. Using time-orientation as one of the fundamental parameters in our manifold, we describe the concept of time and time-series in Special and General Relativity and their intrinsic differences. The notions of A-theory and B-theory will be given mathematical interpretations within the scheme of General Relativity. As a result, in time-orientable spacetimes, the notions of events being in the future and past, which are notions of A-theory, are more fundamental than the notions of events being earlier than or later than other events, which are notions of B-theory. Furthermore, we found that B-theory notions are incompatible with some structures encountered in globally hyperbolic spacetimes, namely past and future inextendible curves.
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First archival date: 2020-05-21
Latest version: 3 (2020-05-25)
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