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

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Abstract
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. By considering orientable spacetimes and defining a time-orientation, we formalize the concepts of a time-series in relativistic spacetimes; A-theory and B-theory are given mathematical descriptions within the formalism of General Relativity. As a result, in time-orientable spacetimes, the notions of events being in the future and in the past, which are notions of A-theory, are found to be more fundamental than the notions of events being earlier than or later than other events, which are notions of B-theory. Furthermore, we find that B-theory notions are incompatible with some structures encountered in globally hyperbolic spacetimes, namely past and future inextendible curves. Hence, GR is favorable to A-theory and the notions of past, present and future.
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First archival date: 2020-05-21
Latest version: 5 (2020-11-10)
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2020-05-21

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