Negative tension branes as stable thin shell wormholes

Abstract

We investigate negative tension branes as stable thin shell wormholes (TSWs) in Reissner–Nordström-(anti) de Sitter spacetimes in d dimensional Einstein gravity. Imposing Z2 symmetry, we construct and classify traversable static TSWs in spherical, planar (or cylindrical) and hyperbolic symmetries. In spherical geometry, we find the higher dimensional counterpart of Barceló and Visser’s wormholes, which are stable against spherically symmetric perturbations. We also find the classes of TSWs in planar and hyperbolic symmetries with a negative cosmological constant, which are stable against perturbations preserving symmetries. In most cases, stable wormholes are found with the combination of an electric charge and a negative cosmological constant. However, as special cases, we find stable wormholes even with vanishing cosmological constant in spherical symmetry and with vanishing electric charge in hyperbolic symmetry.

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

“…Since we obtained Equation (40) by twice squaring Equation 35, there is the possibility that we take wrong solutions which satisfy Equation (40) but do not satisfy Equation (35). However, we can show that this is not the case (see [4] for the proof). By differentiating Equation (40) with respect to τ, we get the equation of motion for the shell asä…”

“…The analysis for k = 0 and k = −1 has also been completed (see [4] for the detail of the analysis). We summarize the stability analysis of the wormholes for all combinations of k, M and q in Tables 1-4 (see [4] for the definitions of N(d, q), S(d, q) and J(d, q) are given in [4]). (1) (2) Figure 16.…”

“…In Einstein gravity, such thin-shell wormholes have been fully investigated in the previous section. In the vacuum case, such thin-shell wormholes are stable against radial perturbations only in the hyperbolically symmetric case with negative mass in the bulk spacetime [4].…”

“…In Section 4, we concentrate on pure tension wormholes in Einstein gravity. This part is based on the work of [4]. We introduce wormholes with a negative-tension brane and we analyze the existence of static solutions, stability and horizon avoidance in spherical, planar and hyperbolic symmetries.…”

Palatini wormholes and energy conditions from the prism of general relativity

“…In fact, a plethora of wormhole solutions beyond GR have been found in a variety of theories, such as in conformal Weyl gravity [58], Kaluza–Klein [59–61], Brans–Dicke [62–65], Gauss–Bonnet [66–69], Lovelock [70, 71] braneworlds [62, 72–74], Hor̆ava–Lifshitz [75, 76], Eddington-inspired Born–Infeld [77–79], metric [80–83] and Palatini [84, 85] approaches of f ( R ) gravity and extensions [86–88], the modified teleparalellism framework [89, 90] or Einstein–Cartan theory [91]. …”