  In this work, we have studied an "exponential form" of spacetime metric:
\begin{equation*} ds^2 = -e^{-\frac{2m}{r}}dt^2 +e^{\frac{2m}{r}}dr^2 +
e^{\frac{2m}{r}}[r^2 d\theta^2 + r^2 \sin^2\theta d\phi^2] \end{equation*} in
some of the viable $f(R)$ gravity models, viz. exponential gravity model,
Starobinsky gravity model, Tsujikawa model and Gogoi-Goswami f(R) gravity
model. Here we have calculated the parameters including energy density,
tangential and radial pressure for these corresponding models of $f(R)$
gravity. Subsequently we have investigated the energy conditions viz. null
energy condition(NEC), weak energy condition(WEC) and strong energy
condition(SEC) for the considered models. We have also explained the suitable
conditions of energy for these models by related plots.
