A note on the stability of generic spherically symmetric thin-shell wormhole supported by a false vacuum

Abstract

In the stability analysis of the Schwarzschild thin-shell wormhole (TSW) performed by Poisson and Visser in Poisson and Visser (1995) the equation of state (EoS) of the surface matter on the throat satisfies β2σ=∂p∂σ in which σ and p are the surface energy density and the surface transverse pressure. In this Letter, we show that β2σ=−1 has to be excluded as it results in the radius of the equilibrium a0=3M a radius which was problematic and later on was treated by Varela in Varela (2015). Furthermore, we present a formalism on the mechanical stability of generic spherically symmetric TSWs supported by a surface energy–momentum tensor of the form σ=−p corresponding to β2σ=−1. Such an EoS with σ>0 describes the so-called vacuum matter or dark energy, however, here it is called false vacuum because σ<0. We obtain the general conditions upon which such a TSW remains stable against a mechanical linear perturbation. In particular, we apply our formalism to first the TSW constructed in the Reissner–Nordström (RN) spacetime and then in the Bronnikov–Zaslavskii (BZ) closed black hole. We show that in both cases stable TSW exists, however, for the former TSW, it corresponds to the non-black hole RN solution.