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Teleparallel gravity shares many qualitative features with general relativity, but differs from it in the following way: whereas in general relativity, gravitation is a manifestation of spacetime curvature, in teleparallel gravity, spacetime is (always) flat. Gravitational effects in this theory arise due to spacetime torsion. It is often claimed that teleparallel gravity is an equivalent reformulation of general relativity. In this paper we question that view. We argue that the theories are not equivalent, by the criterion of categorical equivalence or any stronger criterion, and that teleparallel gravity posits strictly more structure than general relativity.
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The Teleparallel Equivalent of Newton-Cartan Gravity
We construct a notion of teleparallelization for Newton–Cartan theory, and show that the teleparallel equivalent of this theory is Newtonian gravity; furthermore, we show that this result is consistent with teleparallelization in general relativity, and can be obtained by null-reducing the teleparallel equivalent of a five-dimensional gravitational wave solution. This work thus strengthens substantially the connections between four theories: Newton–Cartan theory, Newtonian gravitation theory, general relativity, and teleparallel gravity.
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- Award ID(s):
- 1734155
- PAR ID:
- 10108282
- Date Published:
- Journal Name:
- Classical and quantum gravity
- ISSN:
- 1361-6382
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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