Static and spherically symmetric wormholes in metric-affine theories of gravity
Vittorio De Falco, Salvatore Capozzıello
Abstract
We consider static and spherically symmetric wormhole solutions in extended metric-affine theories of gravity supposing that stability and traversability of these objects can be achieved by means of the more geometric degrees of freedom with respect to general relativity. In particular, we concentrate on $f(R)$ metric, $f(T)$ teleparallel, and $f(Q)$ symmetric teleparallel models, where $f$ is a smooth function of curvature, torsion, and nonmetricity, respectively. In these extended frameworks, $R$, $T$, and $Q$ rule entirely the background geometry without the need to invoke any exotic energy-momentum tensor as matter field source. Assuming that the solution does not present any kind of singularities, we start from the flaring out and null energy conditions to gather together a series of constraints. They allow us to have general indications, which are only necessary but not sufficient and concern only the existence of a throat rather than a global spacetime configuration, to build up then traversable wormholes through a purely geometric approach. The stability cannot be simply assessed via inequalities, because it requires the explicit solution for a detailed analysis.