Carroll expansion of general relativity

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Carroll expansion of general relativity. / Hansen, Dennis; Obers, Niels A.; Oling, Gerben; Sogaard, Benjamin T.

In: SciPost Physics, Vol. 13, No. 3, 055, 08.09.2022.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Hansen, D, Obers, NA, Oling, G & Sogaard, BT 2022, 'Carroll expansion of general relativity', SciPost Physics, vol. 13, no. 3, 055. https://doi.org/10.21468/SciPostPhys.13.3.055

APA

Hansen, D., Obers, N. A., Oling, G., & Sogaard, B. T. (2022). Carroll expansion of general relativity. SciPost Physics, 13(3), [055]. https://doi.org/10.21468/SciPostPhys.13.3.055

Vancouver

Hansen D, Obers NA, Oling G, Sogaard BT. Carroll expansion of general relativity. SciPost Physics. 2022 Sep 8;13(3). 055. https://doi.org/10.21468/SciPostPhys.13.3.055

Author

Hansen, Dennis ; Obers, Niels A. ; Oling, Gerben ; Sogaard, Benjamin T. / Carroll expansion of general relativity. In: SciPost Physics. 2022 ; Vol. 13, No. 3.

Bibtex

@article{1946974e54da4d3e949a54b82ef67427,
title = "Carroll expansion of general relativity",
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 Car-roll 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 = "Dennis Hansen and Obers, {Niels A.} and Gerben Oling and Sogaard, {Benjamin T.}",
year = "2022",
month = sep,
day = "8",
doi = "10.21468/SciPostPhys.13.3.055",
language = "English",
volume = "13",
journal = "SciPost Physics",
issn = "2542-4653",
publisher = "SCIPOST FOUNDATION",
number = "3",

}

RIS

TY - JOUR

T1 - Carroll expansion of general relativity

AU - Hansen, Dennis

AU - Obers, Niels A.

AU - Oling, Gerben

AU - Sogaard, Benjamin T.

PY - 2022/9/8

Y1 - 2022/9/8

N2 - 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 Car-roll 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.

AB - 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 Car-roll 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.

U2 - 10.21468/SciPostPhys.13.3.055

DO - 10.21468/SciPostPhys.13.3.055

M3 - Journal article

VL - 13

JO - SciPost Physics

JF - SciPost Physics

SN - 2542-4653

IS - 3

M1 - 055

ER -

ID: 324369857