Energy–Momentum Pseudotensor and Superpotential for Generally Covariant Theories of Gravity of General Form

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) by the equations of motion. Deformations of the superpotential form for theories with a change in the independent variables in 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.

A gauge-symmetrization method for energy-momentum tensors in high-order electromagnetic field theories

“…In the present study, we will call a EMT symmetric if it is symmetric with respect to tensor indices, and gauge symmetric if it is gauge invariant. To date, much effort has been focused on symmetrizing the EMTs (with respect to tensor indices), while constructing gauge-symmetric EMTs is oftentimes a challenging task for general systems [2][3][4][5][6][7].…”

Editorial to the Special Issue “Selected Papers from the 17th Russian Gravitational Conference—International Conference on Gravitation, Cosmology and Astrophysics (RUSGRAV-17)”

“…Article [2] considers the problem of universal constants and natural systems of units in the spacetime with an arbitrary number of dimensions. The concept of energy-momentum pseudotensor in generally covariant theories of gravity and the possibility of negative energy in generalized Vaidya spacetime are analyzed in [3,4]. We emphasize that the talk of Dr. Vertogradov reflected in the article [4] was awarded by the Organizing Committee of the Conference as the best talk presented by young scientist.…”