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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.
We study the Misner-Sharp mass for the $f(R)$ gravity in an $n$-dimensional (n$geq$3) spacetime which permits three-type $(n-2)$-dimensional maximally symmetric subspace. We obtain the Misner-Sharp mass via two approaches. One is the inverse unified
We obtain the Misner-Sharp mass in the massive gravity for a four dimensional spacetime with a two dimensional maximally symmetric subspace via the inverse unified first law method. Significantly, the stress energy is conserved in this case with a wi
In this article, we seek exact charged spherically symmetric black holes (BHs) with considering $f(mathcal{R})$ gravitational theory. These BHs are characterized by convolution and error functions. Those two functions depend on a constant of integrat
It is nowadays accepted that the universe is undergoing a phase of accelerated expansion as tested by the Hubble diagram of Type Ia Supernovae (SNeIa) and several LSS observations. Future SNeIa surveys and other probes will make it possible to better
We employ gauge-gravity duality to study the backreaction effect of 4-dimensional large-$N$ quantum field theories on constant-curvature backgrounds, and in particular de Sitter space-time. The field theories considered are holographic QFTs, dual to