Static Traversable Wormholes in $f(R, T)=R+2\alpha \ln T$ Gravity

TL;DR

This paper explores static traversable wormholes within a modified gravity framework, deriving exact solutions with minimized exotic matter by employing a novel $f(R,T)$ function and specific relations among pressures and energy density.

Contribution

Introduces a new non-linear $f(R,T)$ gravity model and derives exact wormhole solutions that reduce the need for exotic matter compared to previous models.

Findings

Exact wormhole solutions in $f(R,T)$ gravity are obtained.

Energy conditions are analyzed to minimize exotic matter.

Suitable shape functions are identified for valid wormhole geometries.

Abstract

Traversable wormholes, studied by Morris and Thorne \cite{Morris1} in general relativity, are investigated in this research paper in $f(R,T)$ gravity by introducing a new form of non-linear $f(R,T)$ function. By using this novel function, the Einstein's field equations in $f(R,T)$ gravity are derived. To obtain the exact wormhole solutions, the relations $p_t=\omega\rho$ and $p_r=\sinh(r)p_t$, where $\rho$ is the energy density, $p_r$ is the radial pressure and $p_t$ is the tangential pressure, are used. Other than these relations, two forms of shape function defined in literature are used, and their suitability is examined by exploring the regions of validity of null, weak, strong and dominant energy conditions . Consequently, the radius of the throat or the spherical region, with satisfied energy conditions, is determined and the presence of exotic matter is minimized.