Journal article
Covariant and manifestly projective invariant formulation of Thomas-Whitehead gravity
Physical review. D, Vol.110(8), 084058
10/23/2024
DOI: 10.1103/PhysRevD.110.084058
Abstract
Thomas-Whitehead (TW) gravity is a recently formulated projectively invariant extension of Einstein- Hilbert gravity. Projective geometry was used long ago by Thomas et al. to succinctly package equivalent paths encoded by the geodesic equation. Projective invariance in gravity has further origins in string theory through a geometric action constructed from the method of coadjoint orbits using the Virasoro algebra. A projectively invariant connection arises from this construction, a part of which is known as the diffeomorphism field. TW gravity exploits projective Gauss-Bonnet terms in the action functional to endow the diffeomorphism field with dynamics, while allowing the theory to collapse to general relativity in the limit that the diffeomorphism field vanishes and the connection becomes Levi-Civita. In the original formulation of TW gravity, the diffeomorphism field is projectively invariant but not tensorial and the connection is projectively invariant but not affine. In this paper we reformulate TW gravity in terms of projectively invariant tensor fields and a projectively invariant covariant derivative, derive field equations respecting these symmetries, and show that the field equations obtained are classically equivalent across formulations. This provides a "Rosetta Stone" between this newly constructed covariant and projective invariant formulation of TW gravity and the original formulation that was manifestly projective invariant, but not covariant.
Details
- Title: Subtitle
- Covariant and manifestly projective invariant formulation of Thomas-Whitehead gravity
- Creators
- Tyler Grover - University of IowaKory Stiffler - University of IowaPatrick Vecera - University of California System
- Resource Type
- Journal article
- Publication Details
- Physical review. D, Vol.110(8), 084058
- DOI
- 10.1103/PhysRevD.110.084058
- ISSN
- 2470-0010
- eISSN
- 2470-0029
- Publisher
- Amer Physical Soc
- Number of pages
- 25
- Grant note
- Ford Foundation Professorship of Physics at Brown University
- Language
- English
- Date published
- 10/23/2024
- Academic Unit
- Physics and Astronomy
- Record Identifier
- 9984936505702771
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