$f(\mathsf{R})$ Gravity Wormholes sourced by a Phantom Scalar Field

Abstract

We derive an exact wormhole spacetime supported by a phantom scalar field in the context of $f(\mathsf{R})$ gravity. Without specifying the form of the $f(\mathsf{R})$ function, the scalar field self-interacts with a mass term potential that is derived from the scalar equation and the resulting $f(\mathsf{R})$ model is purely supported by the scalar field and it is free of ghosts and avoids the tachyonic instability.

Accepted for publication in PRD

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• Possibility of the Traversable Wormholes in the Galactic Halos within $4D$ Einstein-Gauss-Bonnet Gravity
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• Polar perturbations of dilaton-Euler-Heisenberg black holes