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Carroll Expansion of General Relativity
by Dennis Hansen, Niels A. Obers, Gerben Oling, Benjamin T. Søgaard
Submission summary
| Authors (as registered SciPost users): | Niels Obers · Gerben Oling |
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| Preprint Link: | https://arxiv.org/abs/2112.12684v4 (pdf) |
| Date accepted: | July 29, 2022 |
| Date submitted: | July 27, 2022, 4:42 a.m. |
| Submitted by: | Gerben Oling |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
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| Approach: | Theoretical |
Abstract
We study the small speed of light expansion of general relativity, utilizing the modern perspective on non-Lorentzian geometry. This is an expansion around the ultra-local Carroll limit, in which light cones close up. To this end, we first rewrite the Einstein-Hilbert action in pre-ultra-local variables, which is closely related to the 3+1 decomposition of general relativity. At leading order in the expansion, these pre-ultra-local variables yield Carroll geometry and the resulting action describes the electric Carroll limit of general relativity. We also obtain the next-to-leading order action in terms of Carroll geometry and next-to-leading order geometric fields. The leading order theory yields constraint and evolution equations, and we can solve the evolution analytically. We furthermore construct a Carroll version of Bowen-York initial data, which has associated conserved boundary linear and angular momentum charges. The notion of mass is not present at leading order and only enters at next-to-leading order. This is illustrated by considering a particular truncation of the next-to-leading order action, corresponding to the magnetic Carroll limit, where we find a solution that describes the Carroll limit of a Schwarzschild black hole. Finally, we comment on how a cosmological constant can be incorporated in our analysis.
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Published as SciPost Phys. 13, 055 (2022)