Wormhole geometries supported by a nonminimal curvature-matter coupling

TL;DR

This paper investigates wormhole solutions in modified gravity with a nonminimal curvature-matter coupling, showing how such couplings can support wormholes by violating energy conditions without exotic matter.

Contribution

It introduces a framework for wormhole geometries in nonminimal curvature-matter coupled gravity and derives an exact solution minimizing energy condition violations.

Findings

Nonminimal coupling supports wormhole geometries.

Exact solutions can reduce null energy condition violations.

Approaches outlined for finding wormhole solutions in complex equations.

Abstract

Wormhole geometries in curvature-matter coupled modified gravity are explored, by considering an explicit nonminimal coupling between an arbitrary function of the scalar curvature, R, and the Lagrangian density of matter. It is the effective stress-energy tensor containing the coupling between matter and the higher order curvature derivatives that is responsible for the null energy condition violation, and consequently for supporting the respective wormhole geometries. The general restrictions imposed by the null energy condition violation are presented in the presence of a nonminimal R-matter coupling. Furthermore, obtaining exact solutions to the gravitational field equations is extremely difficult due to the nonlinearity of the equations, although the problem is mathematically well-defined. Thus, we outline several approaches for finding wormhole solutions, and deduce an exact solution by considering a linear R nonmiminal curvature-matter coupling and by considering an explicit monotonically decreasing function for the energy density. Although it is difficult to find exact solutions of matter threading the wormhole satisfying the energy conditions at the throat, an exact solution is found where the nonminimal coupling does indeed minimize the violation of the null energy condition of normal matter at the throat.