Energy-momentum complexes in f(R) theories of gravity

TL;DR

This paper extends the concept of energy-momentum complexes to f(R) gravity theories, providing a generalized prescription and explicit calculations for specific metrics, addressing a gap in energy localization in modified gravity.

Contribution

It generalizes the Landau-Lifshitz energy-momentum complex to f(R) gravity and computes it for Schwarzschild-de Sitter and other specific models.

Findings

Generalized energy-momentum complex for f(R) gravity.

Explicit calculation for Schwarzschild-de Sitter metric.

Application to popular f(R) models.

Abstract

Despite the fact that modified theories of gravity, in particular the f(R) gravity models have attracted much attention in the last years, the problem of the energy localization in the framework of these models has not been addressed. In the present work the concept of energy-momentum complexes is presented in this context. We generalize the Landau-Lifshitz prescription of calculating the energy-momentum complex to the framework of f(R) gravity. As an important special case, we explicitly calculate the energy-momentum complex for the Schwarzschild-de Sitter metric for a general f(R) theory as well as for a number of specific, popular choices of f(R).