Stress-Energy-Momentum of Affine-Metric Gravity. Generalized Komar Superportential

TL;DR

This paper generalizes the concept of the stress-energy-momentum of gravity to affine-metric theories, showing it reduces to a generalized Komar superpotential for broad classes of connections and Lagrangians.

Contribution

It extends the known reduction of gravitational stress-energy-momentum to the Komar superpotential from Einstein and Palatini theories to more general affine-metric frameworks.

Findings

Stress-energy-momentum reduces to a generalized Komar superpotential.

The result applies to theories with arbitrary connections and covariant Lagrangians.

Provides a unified expression for gravitational energy-momentum in affine-metric gravity.

Abstract

In case of the Einstein's gravitation theory and its first order Palatini reformulation, the stress-energy-momentum of gravity has been proved to reduce to the Komar superpotential. We generalize this result to the affine-metric theory of gravity in case of general connections and arbitrary Lagrangian densities invariant under general covariant transformations. In this case, the stress-energy-momentum of gravity comes to the generalized Komar superpotential depending on a Lagrangian density in a precise way.