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 $x_0=R/M$.
Highlights
Wormholes are hypothetical objects connecting two widely separated regions of space-time or even two different universes
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 fðRÞ cases
We have found the relations between curvature and matter fields at the shell, whose main highlight is the fact that the effective number of degrees of freedom is reduced from two [which are the ones found in general relativity (GR) and in metric fðRÞ gravity] down to one
Summary
Wormholes are hypothetical objects connecting two widely separated regions of space-time or even two different universes. These geometries are obtained by surgically chopping and gluing together suitable patches of the same or different spacetimes at a certain hypersurface or shell in such a way that no horizon is present, rendering a traversable wormhole An advantage of this cut-and-paste construction is that the violations of the energy conditions are typically restricted to the shell, which can subsequently be made as small as possible to keep such violations restricted to a tiny region of the space-time. V contains our conclusion and a discussion of the obtained results and future perspectives
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