Thin-Shell Wormholes in Einstein and Einstein–Gauss–Bonnet Theories of Gravity

Abstract

We review recent works on the possibility for eternal existence of thin-shell wormholes on Einstein and Einstein–Gauss–Bonnet gravity. We introduce thin-shell wormholes that are categorized into a class of traversable wormhole solutions. After that, we discuss stable thin-shell wormholes with negative-tension branes in Reissner–Nordström–(anti) de Sitter spacetimes in d-dimensional Einstein gravity. Imposing Z2 symmetry, we construct and classify traversable static thin-shell wormholes in spherical, planar and hyperbolic symmetries. It is found that the spherical wormholes are stable against spherically symmetric perturbations. It is also found that some classes of wormholes in planar and hyperbolic symmetries with a negative cosmological constant are stable against perturbations preserving symmetries. In most cases, stable wormholes are found with the appropriate combination of an electric charge and a negative cosmological constant. However, as special cases, there are stable wormholes even with a vanishing cosmological constant in spherical symmetry and with a vanishing electric charge in hyperbolic symmetry. Subsequently, the existence and dynamical stability of traversable thin-shell wormholes with electrically neutral negative-tension branes is discussed in Einstein–Gauss–Bonnet theory of gravitation. We consider radial perturbations against the shell for the solutions, which have the Z2 symmetry. The effect of the Gauss–Bonnet term on the stability depends on the spacetime symmetry.

Josephson junction formed in the wormhole space-time from the analysis of the critical temperature of BEC

“…We are going to finally assign the critical value μ c R = m/a c in (20) to μ R in (47), then take the leading order in the expansion of μ c R . For this, we now use two symbols, μ R and μ R :…”

“…• μ R : chemical potential on which the derivative with respect to μ R can act; finally the value m/a c is assigned, • μ R : just a symbol for the value m/a c R , on which the derivative with respect to μ R does not act. 6 In this section we have performed the expansion around μ R = 0 as in (47). However, if we expand around μ R = μ c R , we can obtain the following effective potential:…”

Current Problems and Recent Advances in Wormhole Physics

“…Needless to say that many studies combine some or all of these trends. Nevertheless, it can be more or less conditionally observed that the first trend is represented by the papers [4,13,14,16], the second one by [5,7,11,15], and the third one by [6, 8-10, 12, 17]. Two of the papers are brief reviews [4,9].…”

“…Nevertheless, it can be more or less conditionally observed that the first trend is represented by the papers [4,13,14,16], the second one by [5,7,11,15], and the third one by [6, 8-10, 12, 17]. Two of the papers are brief reviews [4,9]. Thus, Takafumi Kokubu and Tomohiro Harada [4] consider different physical aspects of thin-shell wormholes, both in GR and in Einstein-Gauss-Bonnet gravity, including spherical, planar and hyperbolic symmetries of space-time and the stability issues.…”

“…Two of the papers are brief reviews [4,9]. Thus, Takafumi Kokubu and Tomohiro Harada [4] consider different physical aspects of thin-shell wormholes, both in GR and in Einstein-Gauss-Bonnet gravity, including spherical, planar and hyperbolic symmetries of space-time and the stability issues. Cosimo Bambi and Dejan Stojkovic [9] describe astronomically observable effects of wormholes as possible substitutes of black holes, including gravitational lensing and shadows, possible orbiting star trajectories, accretion disk spectra, and gravitational waves emitted at merges of compact objects, of which one or both are wormholes.…”