Traversable wormholes in the traceless $f(R,T)$ gravity

TL;DR

This paper constructs traversable wormhole solutions within traceless $f(R,T)$ gravity, demonstrating they can satisfy energy conditions and require minimal exotic matter, thus respecting causality without violating physical principles.

Contribution

It introduces a novel wormhole solution in traceless $f(R,T)$ gravity that obeys energy conditions and minimizes exotic matter, expanding the scope of physically plausible wormholes.

Findings

Wormholes satisfy weak energy conditions for specific parameter ranges.

The solutions require arbitrarily small amounts of exotic matter.

Wormholes are traversable and respect causality.

Abstract

We present a traversable wormhole solution using the traceless $f(R,T)$ theory of gravity. In the $f(R,T)$ gravity, the Ricci scalar $R$ in the Einstein-Hilbert action is replaced by a function of $R$ and trace of the energy momentum tensor $T$. The traceless version of the $f(R,T)$ gravity gives rise to a possible wormhole geometry without need for "exotic matter", which violates the principle of causality. Using a physically plausible ansatz for the wormhole's shape function, the traceless field equations lead to compliance with the weak energy condition at very well defined intervals of the coupling constant $\lambda$ in the $f(R,T)=R+2\lambda T$ form. Our solution leads to other well-behaved energy conditions considering some possible values of the parameter $\omega$ in the equation of state $p_r=\omega \rho$, with $p_r$ being the radial pressure and $\rho $ the density. The energy conditions are obeyed in the ranges $\lambda < -4\pi$ and $\omega > -1$. Through the calculation of the Volume Integral Quantifier, one sees that this wormholes can be traversable and respect the causality, since the amount of exotic matter in its interior can be arbitrarily small.