We construct a Hamiltonian for the nonlocal F(R) theory in present work. By this construction, we demonstrate nature of ghost degrees freedom. Finally, find conditions that give rise to ghost-free theories

We provide the modified TOV equations for hydrostatic equilibrium of charged compact stars within metric $f(R)$ gravitational background. adopt MIT bag model EoS dense matter and assume a charge distribution where electric density $\rho_{\rm ch}$ is proportional to standard energy $\rho$. Using Starobinsky model, we explore role $\alpha R^2$ term, $\alpha$ free constant $R$ Ricci scalar, on glo...

We explore the viable $f(R)$ gravity models in FLRW backgrounds with a free spatial curvature parameter $\Omega_{K}$. In our numerical calculation, we concentrate on exponential model of $f(R) = R - \lambda R_{ch}(1-\exp{(-R/R_{ch}}))$, where $R_{ch}$ is characteristic scale, which independent $\Omega_K$, and $\lambda$ corresponds to parameter, while $R_{ch}\lambda=2\Lambda$ $\Lambda$ cosmologi...

In this letter, we consider static black hole in f(R) gravity.We take advantage from corrected entropy and temperature and investigate such black hole. Finally, we study the $ P - V $ critically and phase transition of corrected black hole with respect to entropy and temperature. Here also, we obtain the heat capacity for the static black hole in $ f(R) $ gravity. This calculation help us...