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arXiv · 0910.2387

Generalized Misner-Sharp Energy in f(R) Gravity

Rong-Gen Cai·Li-Ming Cao·Ya-Peng Hu·Nobuyoshi Ohta
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Abstract

We study generalized Misner-Sharp energy in $f(R)$ gravity in a spherically symmetric spacetime. We find that unlike the cases of Einstein gravity and Gauss-Bonnet gravity, the existence of the generalized Misner-Sharp energy depends on a constraint condition in the $f(R)$ gravity. When the constraint condition is satisfied, one can define a generalized Misner-Sharp energy, but it cannot always be written in an explicit quasi-local form. However, such a form can be obtained in a FRW universe and for static spherically symmetric solutions with constant scalar curvature. In the FRW universe, the generalized Misner-Sharp energy is nothing but the total matter energy inside a sphere with radius $r$, which acts as the boundary of a finite region under consideration. The case of scalar-tensor gravity is also briefly discussed.

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Rong-Gen Cai, Li-Ming Cao, Ya-Peng Hu, Nobuyoshi Ohta. 2009-10-28. Generalized Misner-Sharp Energy in f(R) Gravity. https://doi.org/10.1103/physrevd.80.104016

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