Stability of generic cylindrical thin shell wormholes

Abstract

We revisit the stability analysis of cylindrical thin-shell wormholes which have been studied in literature so far. Our approach is more systematic and in parallel to the method which is used in spherically symmetric thin-shell wormholes. The stability condition is summarized as the positivity of the second derivative of an effective potential at the equilibrium radius, i.e., V 00 ða 0 Þ > 0. This may serve as the master equation in all stability problems for the cylindrical thin-shell wormholes.

General formalism for the stability of thin-shell wormholes in $$2+1$$ 2 + 1 dimensions

“…Cylindrical thinshell wormholes have also been studied, which because of their symmetry along their axis constitute a related problem; see for instance Refs. [43][44][45][46].…”

Spherical thin shells in F(R) gravity: construction and stability

“…This formalism has been broadly applied in many different contexts because of its flexibility and simplicity; the stability analysis is easy to perform in highly symmetric situations, and the matter can be confined to the shell. Many researchers have adopted this formalism to model vacuum bubbles and thin layers around black holes [3][4][5][6][7][8][9][10][11], wormholes [12][13][14][15][16][17][18][19][20][21], and gravastars [22][23][24][25], among others.…”

Thin-shell wormholes with charge in F(R) gravity

“…Stability studies of spherically symmetric thin-shell wormholes, with a linearized equation of state at the throat, have been performed under radial perturbations by several authors ( [8][9][10][11][12][13][14][15][16] and references therein). Plane and cylindrical thin-shell wormholes were also analyzed [16][17][18][19][20][21][22][23][24]. The Chaplygin gas and its generalizations a e-mail: eiroa@iafe.uba.ar b e-mail: gfigueroa@iafe.uba.ar were used to model the exotic matter supporting wormholes [25][26][27][28][29][30].…”