Wormhole formation in massive gravity: An analytic description

The present study analyses the wormhole solution both in the dRGT-$f(R,T)$ massive gravity and Einstein massive gravity. In both the models, the anisotropic pressure solution in ultrastatic wormhole geometry gives rise to the shape function that involves massive gravity parameters $\gamma$ and $\Lambda$. However, the terms consisting of $\gamma$ and $\Lambda$ acts in such a way that the spacetime loses asymptotic flatness. Similar to the black hole solution in massive gravity, this inconsistency arises due to the repulsive effect of gravity which can be represented by the photon deflection angle that goes negative after a certain radial distance. It is investigated that the repulsive effect induced in the massive gravitons push the spacetime geometry so strongly that the asymptotic flatness is effected. On the other hand, in this model, one can have a wormhole with ordinary matter at the throat that satisfies all the energy conditions while the negative energy density is sourced by massive gravitons. Finally, using the TOV equation, it is found that the model is stable under the hydrostatic equilibrium condition.