Properties of the wormhole model in de Rham–Gabadadze–Tolley like massive gravity with specific matter density

Abstract

In the conventional method of studying wormhole (WH) geometry, traversability requires the presence of exotic matter, which also provides negative gravity effects to keep the wormhole throat open. In de Rham–Gabadadze–Tolley (dRGT) massive gravity theory, we produce two types of WH solutions in our present paper. We obtain the field equations for exact WH solutions by selecting a static and spherically symmetric metric for the background geometry. We derive the WH geometry completely for the two different choices of redshift functions. The obtained WH solutions violate all the energy conditions, including the null energy condition (NEC). Various plots are used to illustrate the behavior of the wormhole for a suitable range of \(m^2c_1\), where m is the graviton mass. It is observed that the photon deflection angle becomes negative for all values of \(m^2c_1\) as a result of the repulsive action of gravity. It is also shown that the repulsive impact of massive gravitons pushes the spacetime geometry so strongly that the asymptotic flatness is affected. The volume integral quantifier (VIQ) is computed to determine the amounts of matter that violate the null energy condition. The complexity factor of the proposed model is also discussed.