Embedding procedure and wormhole solutions in $f(Q)$ gravity

Abstract

An intriguing solution that appears in General Relativity (GR) but has not been observed so far is the wormhole. This exotic solution describes a topological bridge connecting two distinct universes or two different points in the same universe. It is known that the traversable wormhole solutions violate all the energy conditions in GR, resulting in their instability. In this work, we are going to unveil new wormhole solutions for $f(Q)$ gravity where $Q$ is the non-metricity scalar, which is responsible for the gravitational interaction. The energy conditions to constraint these wormhole solutions were derived using the embedding procedure. This procedure consists of rewriting the density and the pressures of the solutions as those presented by General Relativity. Then, the nontrivial contributions coming from new theories of gravity are embedded into the effective equations for density and pressures. Along with our approach, we carefully analyze two families of $f(Q)$ models and we used two different shape functions to build the wormholes solutions for each of these $f(Q)$ models. We are going to present new scenarios with the possibility of traversable wormholes satisfying SEC or DEC energy conditions in the presence of exotic matter.

EPL published version

References in corpus (10)

• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• Wormhole geometries in f(R) modified theories of gravity
• Detection of the Schwarzschild precession in the orbit of the star S2 near the Galactic centre massive black hole
• Energy Conditions in $f(Q)$ gravity
• Generalized energy conditions in Extended Theories of Gravity
• Wormhole solutions in symmetric teleparallel gravity
• Gravitational waves from bodies orbiting the Galactic Center black hole and their detectability by LISA
• Complete dark energy scenario in $f(Q)$ gravity
• An exponential shape function for wormholes in modified gravity
• Wormhole Structures in Logarithmic-Corrected $R^2$ Gravity

Cited by in corpus (2)

• Coincident f(Q) gravity: black holes, regular black holes and black bounces
• Validity of energy conditions of matter in traversable wormholes under the $f(Q)$ modified gravity theory