General theory of Galilean gravity

Cariglia, Marco

doi:10.1103/physrevd.98.084057

Cited by 21 publications

(13 citation statements)

References 46 publications

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“…The covariant nonrelativistic approximation to GR as introduced by Dautcourt [1] has recently been revisited [2][3][4][5][6][7][8][9]. The approximation amounts to an expansion of the relativistic metric in inverse powers of the speed of light c and for this reason we will refer to it as the large c expansion.…”

Section: Introductionmentioning

confidence: 99%

Oddity in nonrelativistic, strong gravity

2020

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We consider the presence of odd powers of the speed of light c in the covariant nonrelativistic expansion of General Relativity (GR). The term of order c in the relativistic metric is a vector potential that contributes at leading order in this expansion and describes strong gravitational effects outside the (post-)Newtonian regime. The nonrelativistic theory of the leading order potentials contains the full non-linear dynamics of the stationary sector of GR.

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Section: Introductionmentioning

confidence: 99%

Oddity in nonrelativistic, strong gravity

2020

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“…To this end we plan to pursue the analysis of the 1/c expansion in first order formalism in [65]. In this connection see also the references [35,40,41]. A related point that needs to be addressed is the question about the status of the odd powers of 1/c.…”

Section: Discussion and Outlookmentioning

confidence: 99%

“…See also[35] for a non-relativistic action using first-order formalism, and[36] for related perspectives.…”

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confidence: 99%

Non-relativistic gravity and its coupling to matter

Hansen

Hartong

Obers

2020

J. High Energ. Phys.

122

235

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We study the non-relativistic expansion of general relativity coupled to matter. This is done by expanding the metric and matter fields analytically in powers of 1/c 2 where c is the speed of light. In order to perform this expansion it is shown to be very convenient to rewrite general relativity in terms of a timelike vielbein and a spatial metric. This expansion can be performed covariantly and off shell. We study the expansion of the Einstein-Hilbert action up to next-to-next-to-leading order. We couple this to different forms of matter: point particles, perfect fluids, scalar fields (including an off-shell derivation of the Schrödinger-Newton equation) and electrodynamics (both its electric and magnetic limits). We find that the role of matter is crucial in order to understand the properties of the Newton-Cartan geometry that emerges from the expansion of the metric. It turns out to be the matter that decides what type of clock form is allowed, i.e. whether we have absolute time or a global foliation of constant time hypersurfaces. We end by studying a variety of solutions of non-relativistic gravity coupled to perfect fluids. This includes the Schwarzschild geometry, the Tolman-Oppenheimer-Volkoff solution for a fluid star, the FLRW cosmological solutions and anti-de Sitter spacetimes.

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“…In conclusion, the study of nonrelativistic physics through the prism of higher-dimensional relativistic theories opens up many opportunities for further understanding of various aspects of nonrelativistic phenomena and can be useful, for example, in nonrelativistic holography [39,59], which has been gaining attention lately. The Eisenhart Lift Method seems to be a useful tool in this regard, and we hope to conduct further research in this direction.…”

Section: Discussionmentioning

confidence: 99%

Equivalence of a harmonic oscillator to a free particle and Eisenhart lift

Dhasmana,

Sen,

Silagadze

2021

Preprint

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It is widely known in quantum mechanics that solutions of the Schröinger equation (SE) for a linear potential are in one-to-one correspondence with the solutions of the free SE. The physical reason for this correspondence is Einstein's principle of equivalence. What is usually not so widely known is that solutions of the Schrödinger equation with harmonic potential can also be mapped to the solutions of the free Schrödinger equation. The physical understanding of this equivalence is not known as precisely as in the case of the equivalence principle. We present a geometric picture that will link both of the above equivalences with one constraint on the Eisenhart metric.

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General theory of Galilean gravity

Cited by 21 publications

References 46 publications

Oddity in nonrelativistic, strong gravity

Oddity in nonrelativistic, strong gravity

Non-relativistic gravity and its coupling to matter

Equivalence of a harmonic oscillator to a free particle and Eisenhart lift

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