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.

New spherically symmetric wormhole solutions in f(Q)-gravity theory

“…where μ u is the four-velocity, χ u is the unitary space vector pointing in the radial direction, ρ is the energy density, P r is the pressure pointing in the direction of radial pressure, and P t is the pressure pointing in the opposite direction to tangential pressure. Letelier first proposed [38,44] this energy-momentum tensor to explain a two-fluid model in plasma physics, and it has since been used in a variety of different contexts, such as theories for magnetized neutron stars.…”

“…We need a specific shape function to solve field equations for wormhole solutions. Here we have developed a new shape function by taking an account of some shape functions that are considered in the following literature [2,14,38,46,47].The behavior of shape function…”

“…The ringdown period following the merger of binary coalescences would be associated with these gravitational waves. Paul et al [37] suggestion of distinguishing between a black hole and a wormhole geometry using distinguishing characteristics [38] of the accretion disc images is yet another intriguing concept for observation. In some hypotheses, traversable wormholes may provide an alternative means of interplanetary travel, while in others, they are suggested to serve as portals to alternate or even parallel universes [39].…”

Existence of Dark Energy Stars within Lower Mass Gap in the Realm of f(Q)$f(Q)$ Gravity

“…The modified gravities that attracted the researchers are $$f(R)$$ gravity, [ 13,14 ] $$f(G)$$ gravity, [ 15,16 ] $$f(T)$$ gravity, [ 17,18 ] $$f(Q)$$ gravity, [ 19,20 ] $$f(R,\, T)$$ gravity, [ 21,22 ] $$f(R,\, G)$$ gravity [ 23,24 ] etc. In the context of $$f(Q)$$ gravity, models of black hole, [ 25,26 ] wormholes, [ 27,28 ] cosmological models [ 29,30 ] were developed by several researchers.…”

“…The f (R) theory of gravity is the most well-known modified theory of gravity that replaces the Einstein-Hilbert action with a more general action by assuming that the gravitational action is given by any arbitrary function of the Ricci scalar R. The modified gravities that DOI: 10.1002/prop.202300074 attracted the researchers are f (R) gravity, [13,14] f (G) gravity, [15,16] f (T) gravity, [17,18] f (Q) gravity, [19,20] f (R, T) gravity, [21,22] f (R, G) gravity [23,24] etc. In the context of f (Q) gravity, models of black hole, [25,26] wormholes, [27,28] cosmological models [29,30] were developed by several researchers. Dark energy is a potential candidate to prevent compact objects from collapsing into singularities due to gravity.…”