Exponential wormhole, its quasinormal modes, and study in logarithmic f(R) gravity

We have investigated the quasinormal modes of “exponential wormhole” using 3rd-order WKB approximation. Following that, we have explored the metric in the logarithmic $f\left(R\right)$ gravity using a cubic gravity term inside the $f\left(R\right)$ function. We determined the parameters for the logarithmic $f\left(R\right)$ gravity model, which include energy density, tangential, and radial pressure. Afterward, we explored the energy conditions for the proposed model through related plots. We have used trivial techniques to constrain the free parameters of the logarithmic $f\left(R\right)$ gravity. We showed the appropriate stability criteria using related graphs. Also, we discovered that the exponential wormhole satisfies some of the required energy barriers in the Logarithmic $f\left(R\right)$ gravity without disturbing any flare-out or stability constraints. We additionally studied the stability of the exponential wormhole in the logarithmic $f\left(R\right)$ gravity through the Tolman–Oppenheimer–Volkoff(TOV) equation and found some interesting nature of the space–time. The logarithmic f(R) gravity model is convenient for the exponential wormhole’s existence, even if there are certain limitations on the parameter ranges of the $f\left(R\right)$ gravity model.