Wormhole solutions in generalized Rastall gravity

TL;DR

This paper finds new wormhole solutions in generalized Rastall gravity where the matter satisfies physical energy conditions, and explores their gravitational lensing effects, suggesting possible observable signatures without requiring exotic matter.

Contribution

It introduces novel wormhole solutions in generalized Rastall gravity with physically reasonable matter, including cases with zero and nonzero redshift functions, and analyzes their lensing properties.

Findings

Wormhole solutions obey energy conditions at the throat and throughout spacetime.

Asymptotically flat wormholes can exist without exotic matter in GRG.

Throat acts as a photon sphere with large light deflection.

Abstract

In the present work, we seek for static spherically symmetric solutions representing wormhole configurations in generalized Rastall gravity (GRG). In this theory, a varying coupling parameter could act as dark energy (DE) and thus, it can be considered as responsible for the current accelerated expansion of the universe. We consider an anisotropic energy momentum tensor (EMT) as the supporting source for wormhole structure and further assume that there exists a linear relation between radial and tangential pressures and energy density. We therefore obtain two classes of solutions to the field equations of GRG, including the solutions with zero and nonzero redshift functions. For these solutions we find that the matter distribution obeys the physical reasonability conditions, i.e., the flare-out and the weak (WEC) and null (NEC) energy conditions either at the throat and throughout the spacetime. The conditions on physical reasonability of the wormhole solutions put restrictions on model parameters. Hence, in the framework of GRG, asymptotically flat wormhole configurations can be built without the need of exotic matter. Gravitational lensing effects of the obtained solutions are also discussed and it is found that the throat of wormhole can effectively act as a photon sphere near which the light deflection angle takes arbitrarily large values.