Morris–Thorne wormholes in modified f(R, T) gravity

Abstract

Wormhole solutions obtained by Morris and Thorne (MT) in general relativity (GR) is investigated in a modified theory of gravity. In the gravitational action, we consider f(R, T) which is a function of the Ricci scalar (R) and the trace of the energy-momentum tensor (T). In the framework of a modified gravity described by $$f(R,T)=R+\alpha R^{2}+\lambda T^{\beta }$$ , where $$\alpha $$ , $$\beta $$ and $$\lambda $$ are coupling constants, MT wormhole (WH) solutions with normal matter are obtained for a relevant shape function. We have considered two different values of $$\beta $$ leading to two forms of f(R, T)-gravity. The energy conditions are probed at the throat and away from the throat of the WH. It is found that the coupling parameters, $$\alpha $$ and $$\lambda $$ in the gravitational action play an important role in deciding the matter composition in the wormholes. It is found that for a given $$\lambda $$ , WH exists in the presence of exotic matter at the throat when $$\alpha <0$$ . It is demonstrated here that WH exists even without exotic matter for $$\alpha >0$$ in the modified gravity. Two different shape functions are considered to obtain WH solutions that are permitted with or without exotic matter. It is noted that in a modified f(R, T) gravity MT WH is permitted with normal matter which is not possible in GR. It is demonstrated that a class of WH solutions exist with anisotropic fluid for $$\lambda \ne -8\pi $$ . However, for flat asymptotic regions with anisotropic fluids WH solutions cannot be realized when $$\lambda =-8\pi $$ . All the energy conditions are found consistent with the hybrid shape function indicating existence of WH even with normal matter for $$\lambda \rightarrow 0$$ .