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

13 pages, published version

References in corpus (19)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Disappearing cosmological constant in f(R) gravity
• Class of viable modified $f(R)$ gravities describing inflation and the onset of accelerated expansion
• Wormhole geometries in f(R) modified theories of gravity
• Energy conditions in f(R)-gravity
• Thin accretion disks in f(R) modified gravity models
• Higher dimensional charged $f(R)$ black holes
• On the Stability of a class of Modified Gravitational Models
• Wormhole throats in $R^m$ gravity
• Evolving wormhole geometries within nonlinear electrodynamics
• Magnetic black universes and wormholes with a phantom scalar
• Cylindrical wormholes
• Spherically Symmetric Solutions to Fourth-Order Theories of Gravity
• f(R) Gravity: From the Pioneer Anomaly to the Cosmic Acceleration
• Energy conditions in f(R) gravity and Brans-Dicke theories
• Black hole entropy in modified gravity models
• Energy-momentum complexes in f(R) theories of gravity
• Topological electro-vacuum solutions in extended gravity

Cited by in corpus (8)

• Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A${}^{\ast }$
• Black holes with scalar hair in light of the Event Horizon Telescope
• Mimetic gravity: a review of recent developments and applications to cosmology and astrophysics
• A special class of solutions in $F(R)$-gravity
• Traversable wormholes with double layer thin shells in quadratic gravity
• Interpenetrating subspaces as a funnel to extra space
• Can Holographic dark energy increase the mass of the wormhole?
• Static Spherically Symmetric solutions in a subclass of Horndeski theories of gravity