Energy Distribution in f(R) Gravity

TL;DR

This paper examines energy distribution in f(R) gravity using the Landau-Lifshitz complex, analyzing plane symmetric solutions and cosmic string spacetime for various f(R) models, and discusses stability and scalar curvature conditions.

Contribution

It introduces a generalized energy-momentum complex approach to evaluate energy in f(R) gravity and applies it to specific models and spacetimes, addressing the energy problem in modified gravity.

Findings

Energy density computed for specific f(R) models

Conditions for constant scalar curvature and stability discussed

Energy distribution analyzed for cosmic string spacetime

Abstract

The well-known energy problem is discussed in f(R) theory of gravity. We use the generalized Landau-Lifshitz energy-momentum complex in the framework of metric f(R) gravity to evaluate the energy density of plane symmetric solutions for some general f(R) models. In particular, this quantity is found for some popular choices of f(R) models. The constant scalar curvature condition and the stability condition for these models are also discussed. Further, we investigate the energy distribution of cosmic string spacetime.