Looking for empty topological wormhole spacetimes in $F(R)$-modified gravity

TL;DR

This paper investigates the existence and difficulty of finding empty wormhole solutions in $F(R)$ gravity, a modified theory of gravity that extends General Relativity, highlighting the challenges and partial solutions in this area.

Contribution

It explains why empty wormhole spacetimes are hard to find in $F(R)$ gravity and provides some explicit solutions in simple cases.

Findings

Few solutions derived in simple cases

Implicit form obtained in complex cases

Highlights difficulty of finding wormholes in $F(R)$ gravity

Abstract

Much attention has been recently devoted to modified theories of gravity in the attempt to efficiently describe both early inflation and late-time acceleration of our universe without referring to the cosmological constant or other ad hoc kinds of fluids. The simplest models overcome General Relativity simply by replacing $R$ with $F(R)$ in the Einstein--Hilbert action. Unfortunately, such models typically lack most of the beautiful solutions discovered in Einstein's gravity. Nonetheless, in $F(R)$ gravity, it has been possible to get at least few black holes, but still we do not know any empty wormhole-like spacetime solution. The present paper aims to explain why it is so hard to get such solutions (given that they exist). Few solutions are derived in the simplest cases while only an implicit form has been obtained in the non-trivial case.