Energy Constraints for Evolving Spherical and Hyperbolic Wormholes in $f(R,T)$ Gravity

TL;DR

This paper investigates energy condition bounds for spherical and hyperbolic wormholes within $f(R,T)$ gravity, analyzing how different parameters affect energy density and pressure conditions through graphical methods.

Contribution

It formulates field equations for wormholes in $f(R,T)$ gravity and analyzes energy conditions for various geometries and parameter choices, providing new insights into wormhole energy constraints.

Findings

Energy density is positive for certain parameter ranges in spherical wormholes.

Radial pressure conditions vary, being negative at the throat for spherical cases.

In hyperbolic wormholes, energy density remains positive for negative $mbda$.

Abstract

The primary objective of this article is to study the energy condition bounds for spherical and hyperbolic wormholes in well-known $f(R,T)$ theory of gravity. For this purpose, we formulate the field equations for spherically and pseudospherically geometries using anisotropic matter and linear form of generic function $f(R,T)$. By imposing different conditions on radial and tangential pressures or by adopting some known choices for red shift and shape functions, we present the graphical analysis of energy conditions for both spherically and pseudospherically symmetric wormholes. It is seen that energy density for spherically symmetric wormhole is always positive for $\lambda>-4\pi$ and $\lambda<-8\pi$, while the energy conditions for radial pressure are negative at throat. Likewise, in case of pseudospherically symmetric wormhole, it is observed that energy density is always positive for negative $\lambda$, however conditions based on radial pressure may be positive or negative for the considered different cases.