Scalar wormholes with nonminimal derivative coupling

Abstract

We consider static spherically symmetric wormhole configurations in a gravitational theory of a scalar field with a potential $V(\varphi )$ and nonminimal derivative coupling to the curvature describing by the term $(\epsilon g_{\mu \nu }+\kappa G_{\mu \nu }){\varphi }^{,\mu }{\varphi }^{,\nu }$ 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 $V(\varphi )=0$ (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 $\kappa <{\kappa }_1\le 0$, otherwise one or both wormhole masses are negative. In conclusion, we give qualitative arguments that a wormhole configuration with positive masses could be stable.

17 pages, 8 figures

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