Wormholes in Poincar\`{e} gauge theory of gravity

TL;DR

This paper investigates static spherically symmetric wormhole solutions within Poincaré gauge theory of gravity, demonstrating that such wormholes can exist without exotic matter and analyzing their observational signatures through gravitational lensing.

Contribution

It introduces a class of wormhole solutions in Poincaré gauge theory with spinless matter, showing they satisfy energy conditions and exhibit unique lensing features.

Findings

Wormholes without exotic matter are possible in PGT.

The solutions obey weak and null energy conditions at the throat.

Gravitational lensing shows diverging, zero, and negative deflection angles.

Abstract

In the present work, we {study} static spherically symmetric solutions representing wormhole configurations in Poincar\`{e} gauge theory ({{\sf PGT}}). The gravitational sector of the Lagrangian is chosen as a subclass of {\sf PGT} Lagrangians for which, the spin-$0^+$ is the only propagating torsion mode. The spacetime torsion in {\sf PGT} has a dynamical nature even in the absence of intrinsic angular momentum (spin) of matter, hence, {torsion can play a principal role in the case of usual spin-less gravitating systems. We therefore} consider a spin-less matter distribution with an anisotropic energy momentum tensor ({\sf EMT}) as the supporting source for wormhole structure {to obtain a class of zero tidal force wormhole solutions.} It is seen that the matter distribution obeys the physical reasonability conditions, i.e., the weak ({\sf WEC}) and null ({\sf NEC}) energy conditions either at the throat and throughout the spacetime. We further consider varying equations of state in radial and tangential directions via definitions $w_r(r)=p_r(r)/\rho(r)$ and $w_t(r)=p_t(r)/\rho(r)$ and {investigate} the behavior of state parameters {at the throat of wormhole}. We observe that our solutions allow for wormhole configurations without the need of exotic matter. Observational features of the wormhole solutions are also discussed utilizing gravitational lensing effects. It is found that the light deflection angle diverges at the throat (which indeed, effectively acts as a photon sphere) and can get zero and negative values depending on the model parameters.