Generalized Misner-Sharp Energy in f(R) Gravity

Understand

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.