Carroll expansion of general relativity

Hansen, DennisETH, Inst Theoret Phys, Wolfgang Pauli Str 27, CH-8093 Zurich, Switzerland. (författare)

QC 20221108
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.

Obers, Niels A.Stockholms universitet,KTH,Nordic Institute for Theoretical Physics NORDITA,Stockholm Univ, Hannes Alfvens Vag 12, SE-10691 Stockholm, Sweden.;Univ Copenhagen, Niels Bohr Inst, Blegdamsvej 17, DK-2100 Copenhagen O, Denmark.,Nordiska institutet för teoretisk fysik (Nordita),University of Copenhagen, Denmark(Swepub:su)niob8745 (författare)
Oling, GerbenStockholms universitet,Nordiska institutet för teoretisk fysik (Nordita),University of Copenhagen, Denmark,NORDITA SU ;Stockholm Univ, Hannes Alfvens Vag 12, SE-10691 Stockholm, Sweden.;Univ Copenhagen, Niels Bohr Inst, Blegdamsvej 17, DK-2100 Copenhagen O, Denmark.(Swepub:su)geol8346 (författare)
Sogaard, Benjamin T.Univ Copenhagen, Niels Bohr Inst, Blegdamsvej 17, DK-2100 Copenhagen O, Denmark.;Princeton Univ, Dept Phys, Princeton, NJ 08544 USA. (författare)
ETH, Inst Theoret Phys, Wolfgang Pauli Str 27, CH-8093 Zurich, Switzerland.Nordic Institute for Theoretical Physics NORDITA (creator_code:org_t)

Av författaren/redakt...: Hansen, Dennis; Obers, Niels A.; Oling, Gerben; Sogaard, Benjami ...

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