Torsional Newton–Cartan gravity from the large c expansion of general relativity

Bleeken, Dieter Van den

doi:10.1088/1361-6382/aa83d4

Cited by 103 publications

(228 citation statements)

References 19 publications

(69 reference statements)

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“…This has severe implications: the result of gauging the Bargmann algebra will in general not coincide with the 1/c 2 expansion of general relativity [2]! To see how strong field effects are encoded into the non-relativistic limit of general relativity, we define the following covariant 1/c 2 expansion (where c is the slope of the light cone in tangent space) of the Lorentzian metric 1 g µν [3,12]:…”

mentioning

confidence: 99%

Gravity between Newton and Einstein

Hansen

Hartong

Obers

2019

Int. J. Mod. Phys. D

128

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Statements about relativistic effects are often subtle. In this essay we will demonstrate that the three classical tests of general relativity, namely perihelion precession, deflection of light and gravitational redshift, are passed perfectly by an extension of Newtonian gravity that includes gravitational time dilation effects while retaining a non-relativistic causal structure. This non-relativistic gravity theory arises from a covariant large speed of light expansion of Einstein's theory of gravity that does not assume weak fields and which admits an action principle.

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mentioning

confidence: 99%

Gravity between Newton and Einstein

Hansen

Hartong

Obers

2019

Int. J. Mod. Phys. D

128

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“…Above we used the boost invariant covariant derivatives (3.13). We may fix arbitrary coefficients in equations (5.4) by comparing it with a similar result in [33]. In four dimensions (d = 3) the similar equation of [33] is;…”

Section: Ehlers Conditionsmentioning

confidence: 97%

“…In the presence of twistless torsion i.e. b a = 0 the equations of motion are given in [1,33,34]. In [1] these equations were obtained by exploiting the non-relativistic conformal method starting from a Schrödinger field theory in flat spacetime.…”

Section: Poisson's Equationmentioning

confidence: 99%

Covariant Poisson’s equation in torsional Newton-Cartan gravity

Abedini¹,

Afshar²,

Ghodsi³

2019

J. High Energ. Phys.

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We derive the covariant Poisson's equation of (d + 1)-dimensional Newton-Cartan gravity with (twistless) torsion by applying the 'non-relativistic conformal method' introduced in [1]. We apply this method on-shell to a Schrödinger field theory on the curved Newton-Hooke background. The covariance of the field equation in the presence of the non-relativistic cosmological constant, entails fixing all coefficients in the covariant Poisson's equation for (twistless) torsional Newton-Cartan gravity. We further derive Ehlers conditions and an equation associated to the torsion in this method.

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“…These conditions do not depend on the choice of longitudinal frame and, thus, they refer to the structure of the metrics τ and h. In fact, when studying pNC geometries as the leading terms of a covariant expansion of General Relativity [26][27][28], it is useful to rewrite the results in Proposition 3.2 in terms of such metrics and in a general coordinate chart as follows…”

Section: The Equivalence Problem In Non-relativistic Structuresmentioning

confidence: 99%

p-brane Newton–Cartan geometry

Pereñiguez

2019

Journal of Mathematical Physics

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We provide a formal definition of p-brane Newton-Cartan (pNC) geometry and establish some foundational results. Our approach is the same followed in the literature for foundations of Newton-Cartan Gravity. Our results provide control of aspects of pNC geometry that are otherwise unclear when using the usual gauge language of non-relativistic theories of gravity.In particular, we obtain a set of necessary and sufficient conditions that a pNC structure must satisfy in order to admit torsion-free, compatible affine connections, and determine the space formed by the latter. This is summarised in Theorem 3.1. Since pNC structures interpolate between Leibnizian structures for p = 0 and Lorentzian structures for p = d − 1 (with d the dimension of the spacetime manifold), the present work also constitutes a generalisation of results of Newton-Cartan and (pseudo-) Riemannian

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Torsional Newton–Cartan gravity from the large c expansion of general relativity

Cited by 103 publications

References 19 publications

Gravity between Newton and Einstein

Gravity between Newton and Einstein

Covariant Poisson’s equation in torsional Newton-Cartan gravity

p-brane Newton–Cartan geometry

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