Freud’s superpotential in general relativity and in Einstein-Cartan theory

Böhmer, Christian G.; Hehl, Friedrich W.

doi:10.1103/physrevd.97.044028

Cited by 7 publications

(6 citation statements)

References 34 publications

(37 reference statements)

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“…Equivalently in terms of tensors, the object with vanishing (Levi-Civita) divergence is T eff µν as defined in (22), and it provides the conserved energy-momentum tensor of the theory. 4 This simple observation is well-known in the literature, see [12,13,26] (where it is referred to as 'combined energy-momentum tensor'), and can be taken to provide the basis of energy conservation in Einstein-Cartan theory.…”

Section: Noether Identities and Conservation Lawsmentioning

confidence: 93%

“…There are three problems that we can see with this construction. First, a Killing vector is metricgeodesic, but in general not geodesic with respect to the torsion-full connection, since from (13) we see that…”

Section: Non-equilibrium Approachmentioning

confidence: 98%

“…To prove this identity, we start from (27b). On the left-hand side, we split the connection into Levi-Civita plus contorsion, see (13), obtaining…”

Section: B Index Jugglersmentioning

confidence: 99%

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Spacetime thermodynamics with contorsion

2018

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We prove that a conserved effective energy-momentum tensor for Einstein-Cartan theory can be identified from the Noether identities of the matter Lagrangian, using the torsion field equations relating them. More precisely, a one-parameter family labelled by the Immirzi parameter. We use this result and the contorsion description to show that Jacobson's thermodynamical derivation of the Einstein equations follows as in the metric theory, namely from the equilibrium Clausius relation and the fact that a Killing horizon is metric-geodetic. Our derivation works for an arbitrary torsion field. In the course of our discussion we review the laws of black hole mechanics and their dependence on torsion.

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Section: Noether Identities and Conservation Lawsmentioning

confidence: 93%

Section: Non-equilibrium Approachmentioning

confidence: 98%

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Spacetime thermodynamics with contorsion

2018

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“…φ = −ψ. Only scalars and vectors contribute to either (153) or (154) and there is no energy due to tensor modes. We will have a closer look at the transverse-traceless components h ij , which are the only components that may propagate in vacuum.…”

Section: A Linear Perturbationsmentioning

confidence: 99%

Energy and entropy in the Geometrical Trinity of gravity

Gomes¹,

Jiménez²,

Koivisto³

2022

Preprint

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All energy is gravitational energy. That is the consequence of the equivalence principle, according to which gravity is the universal interaction. The physical charges of this interaction have remained undisclosed, but the Advent of the Geometrical Trinity opened a new approach to this foundational problem. Here it is shown to provide a background-independent unification of the previous, noncovariant approaches of Bergmann-Thomson, Cooperstock, Einstein, von Freud, Landau-Lifshitz, Papapetrou and Weinberg. First, the Noether currents are derived for a generic Palatini theory of gravity coupled with generic matter fields, and then the canonical i.e. the unique charges are robustly derived and analysed, particularly in the metric teleparallel and the symmetric teleparallel versions of General Relativity. These results, and their application to black holes and gravitational waves, are new.

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“…Previously, Wallner and Thirring [1,2] explicitly showed that using the expression for the Thirring 2-forms, it is possible to obtain sundry energy definitions of energy, given by for example, Freud [3], Møller [4,5], and Landau and Lifschitz [6]. See also the recent paper by Böhmer and Hehl [7]. Here, we elaborate on the reformulation of the Abbott-Deser energy definition in terms of differential forms that helps to gain further insight into complicated mathematical expressions.…”

mentioning

confidence: 99%