Energy-momentum pseudotensor and superpotential for generally covariant theories of gravity of general form
arXiv:2010.07073 · doi:10.3390/universe6100173
Abstract
The current paper is devoted to the investigation of the general form of the energy-momentum pseudotensor (pEMT) and the corresponding superpotential for the wide class of theories. The only requirement for such a theory is the general covariance of the action without any restrictions on the order of derivatives of the independent variables in it or their transformation laws. As a result of the generalized Noether procedure, we obtain a recurrent chain of the equations, which allows one to express canonical pEMT as a divergence of the superpotential. The explicit expression for this superpotential is also given. We discuss the structure of the obtained expressions and the conditions for the derived pEMT conservation laws to be satisfied independently (fully or partially) of the equations of motion. Deformations of the superpotential form for theories with a change of the independent variables in the action are also considered. We apply these results to some interesting particular cases: General Relativity and its modifications, particularly mimetic gravity and Regge-Teitelboim embedding gravity.
arXiv commentLaTeX, 19 pages
References in corpus (30)
- Soft Hair on Black Holes
- Towards singularity and ghost free theories of gravity
- Covariant theory of asymptotic symmetries, conservation laws and central charges
- The Relation between Physical and Gravitational Geometry
- Mimetic Dark Matter
- Mimetic gravity: a review of recent developments and applications to cosmology and astrophysics
- Cosmology with Mimetic Matter
- On the recently proposed Mimetic Dark Matter
- Relativistic conservation laws and integral constraints for large cosmological perturbations
- Currents and Superpotentials in classical gauge invariant theories I. Local results with applications to Perfect Fluids and General Relativity
- The Energy-Momentum Tensor for the Gravitational Field
- The two faces of mimetic Horndeski gravity: disformal transformations and Lagrange multiplier
- Dark matter as a ghost free conformal extension of Einstein theory
- Geodetic Brane Gravity
- Noether's Second Theorem and Ward Identities for Gauge Symmetries
- On the quantisation of gravity by embedding spacetime in a higher dimensional space
- Canonical formulation of the embedded theory of gravity equivalent to Einstein's General Relativity
- Relativistic Conservation Laws on Curved Backgrounds and the Theory of Cosmological Perturbations
- Ostrogradski approach for the Regge-Teitelboim type cosmology
- From the Embedding Theory to General Relativity in a result of inflation
- Gravity as a field theory in flat space-time
- Embedding theory as new geometrical mimetic gravity
- Forms of action for perfect fluid in General Relativity and mimetic gravity
- The gauge invariance of general relativistic tidal heating
- Energy Localization Invariance of Tidal Work in General Relativity
- Modifications of gravity via differential transformations of field variables
- The approach to gravity as a theory of embedded surface
- Energy-Momentum of the Gravitational Field: Crucial Point for Gravitation Physics and Cosmology
- Exact relation between canonical and metric energy-momentum tensors for higher derivative tensor field theories
- Gravitational energy in the framework of embedding and splitting theories