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

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.

arXiv commentRevision submitted to IJMPD

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• Stealth Ellis Wormholes In Horndeski theories
• Energy Constraints for Evolving Spherical and Hyperbolic Wormholes in $f(R,T)$ Gravity
• Some Specific Wormhole Solutions in Extended $f(R,G,T)$ Gravity
• Geodesics in Generalised Ellis-Bronnikov Spacetime Embedded in Warped 5D Background
• Dynamical Wormhole Solutions in $f(R,T)$ Gravity
• Damour-Solodukhin Wormhole as a Black Hole Mimicker: The Role of Observers' Location