Study of exponential wormhole metric in $f(R)$ gravity

TL;DR

This paper explores an exponential wormhole metric within various $f(R)$ gravity models, analyzing energy conditions and physical parameters to understand their viability and characteristics.

Contribution

It introduces an exponential wormhole metric in $f(R)$ gravity and evaluates energy conditions across multiple models, providing new insights into their physical plausibility.

Findings

Energy density and pressure parameters calculated for each model.

Energy conditions such as NEC, WEC, SEC analyzed and visualized.

Models satisfy certain energy conditions under specific parameters.

Abstract

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.