Generalized Misner-Sharp Energy in f(R) Gravity

Details Generalized Misner-Sharp Energy in f(R) Gravity Generalized Misner-Sharp Energy in f(R) Gravity

2009-10-13

arxiv.org/abs/0910.2387v2

Phys.Rev.D80:104016,2009

Physics

High Energy Physics

High Energy Physics - Theory

Revtex, 17 pages, v2: some references added, to appear in PRD

Scientific paper

10.1103/PhysRevD.80.104016

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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