Structure and stability of traversable thin-shell wormholes in Palatini $f(\mathcal{R})$ gravity

TL;DR

This paper investigates the structure and stability of traversable thin-shell wormholes within Palatini $f( ext{R})$ gravity, revealing unique properties of the shell's energy and conditions for stability in charged configurations.

Contribution

It introduces a junction formalism for Palatini $f( ext{R})$ gravity, showing the shell's degrees of freedom are reduced and that the energy density can vary freely, unlike in general relativity.

Findings

Shell's equation of state is that of massless fields.

Surface energy density can be zero or of any sign.

Reissner-Nordström wormholes can be stable with positive energy density.

Abstract

We study the structure and stability of traversable wormholes built as (spherically symmetric) thin shells in the context of Palatini $f(\mathcal{R})$ gravity. Using a suitable junction formalism for these theories we find that the effective number of degrees of freedom on the shell is reduced to a single one, which fixes the equation of state to be that of massless stress-energy fields, contrary to the general relativistic and metric $f(R)$ cases. Another major difference is that the surface energy density threading the thin-shell, needed in order to sustain the wormhole, can take any sign, and may even vanish, depending on the desired features of the corresponding solutions. We illustrate our results by constructing thin-shell wormholes by surgically grafting Schwarzschild space-times, and show that these configurations are always linearly unstable. However, surgically joined Reissner-Nordstr\"om space-times allow for linearly stable, traversable thin-shell wormholes supported by a positive energy density provided that the (squared) mass-to-charge ratio, given by $y=Q^2/M^2$, satisfies the constraint $1<y<9/8$ (corresponding to overcharged Reissner-Nordstr\"om configurations having a photon sphere) and lies in a region bounded by specific curves defined in terms of the (dimensionless) radius of the shell $x_0=R/M$.