Scalar wormholes with nonminimal derivative coupling

TL;DR

This paper explores static, spherically symmetric wormholes in a scalar-tensor gravity theory with nonminimal derivative coupling, demonstrating the existence of traversable solutions with various mass configurations and discussing their potential stability.

Contribution

It introduces new traversable wormhole solutions in a scalar-tensor theory with nonminimal derivative coupling, analyzing their mass properties and stability prospects.

Findings

Traversable wormholes can have positive or negative masses depending on coupling parameters.

Both phantom and ordinary scalar fields can support wormhole geometries.

Positive mass wormholes are potentially stable according to qualitative arguments.

Abstract

We consider static spherically symmetric wormhole configurations in a gravitational theory of a scalar field with a potential $V(\phi)$ and nonminimal derivative coupling to the curvature describing by the term $(\epsilon g_{\mu\nu} + \kappa G_{\mu\nu}) \phi^{,\mu}\phi^{,\nu}$ in the action. We show that the flare-out conditions providing the geometry of a wormhole throat could fulfilled both if $\epsilon=-1$ (phantom scalar) and $\epsilon=+1$ (ordinary scalar). Supposing additionally a traversability, we construct numerical solutions describing traversable wormholes in the model with arbitrary $\kappa$, $\epsilon=-1$ and $V(\phi)=0$ (no potential). The traversability assumes that the wormhole possesses two asymptotically flat regions with corresponding Schwarzschild masses. We find that asymptotical masses of a wormhole with nonminimal derivative coupling could be positive and/or negative depending on $\kappa$. In particular, both masses are positive only provided $\kappa<\kappa_1\le0$, otherwise one or both wormhole masses are negative. In conclusion, we give qualitative arguments that a wormhole configuration with positive masses could be stable.