The energy-momentum complex in non-local gravity
arXiv:2301.04023 · doi:10.1142/S0219887823501773
Abstract
In General Relativity, the issue of defining the gravitational energy contained in a given spatial region is still unresolved, except for particular cases of localized objects where the asymptotic flatness holds for a given spacetime. In principle, a theory of gravity is not self-consistent, if the whole energy content is not uniquely defined in a specific volume. Here we generalize the Einstein gravitational energy-momentum pseudotensor to non-local theories of gravity where analytic functions of the non-local integral operator are taken into account. We apply the Noether theorem to a gravitational Lagrangian, supposed invariant under the one-parameter group of diffeomorphisms, that is, the infinitesimal rigid translations. The invariance of non-local gravitational action under global translations leads to a locally conserved Noether current, and thus, to the definition of a gravitational energy-momentum pseudotensor, which is an affine object transforming like a tensor under affine transformations. Furthermore, the energy-momentum complex remains locally conserved, thanks to the non-local contracted Bianchi identities. The continuity equations for the gravitational pseudotensor and the energy-momentum complex, taking into account both gravitational and matter components, can be derived. Finally, the weak field limit of pseudotensor is performed to lowest order in metric perturbation in view of astrophysical applications.
17 pages
References in corpus (16)
- Dynamics of Nonlocal Cosmology
- Newtonian limit of nonlocal cosmology
- Screening of cosmological constant in non-local gravity
- Non-Local Gravity Cosmology: an Overview
- Energy-momentum complexes in f(R) theories of gravity
- Non-Local Gravity Wormholes
- Nonlocal Cosmology II --- Cosmic acceleration without fine tuning or dark energy
- Considerations on gravitational waves in higher-order local and non-local gravity
- Gravitational waves in non-local gravity
- Non-Local Curvature Gravity Cosmology via Noether Symmetries
- Gravitational energy-momentum pseudo-tensor in Palatini and metric gravity
- Gravitational radiation in higher order non-local gravity
- Nonlocal de Sitter gravity and its exact cosmological solutions
- New Cosmological Solutions of a Nonlocal Gravity Model
- Energy-Momentum Complex in Higher Order Curvature-Based Local Gravity
- Quantum interference in external gravitational fields beyond General Relativity