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Carroll Expansion of General Relativity
by Dennis Hansen, Niels A. Obers, Gerben Oling, Benjamin T. Søgaard
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Niels Obers · Gerben Oling |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2112.12684v4 (pdf) |
| Date accepted: | 2022-07-29 |
| Date submitted: | 2022-07-27 04:42 |
| Submitted by: | Oling, Gerben |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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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.
Author comments upon resubmission
List of changes
The paragraph directly below Equation (2.30) has been rewritten.
Published as SciPost Phys. 13, 055 (2022)