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.