Probing global aspects of a geometry by the self-force on a charge: Cylindrical thin-shell wormholes

Abstract

We obtain the self-interaction for a point charge in the space-time of a cylindrical thin-shell wormhole connecting two identical locally flat geometries with a constant deficit angle. Although this wormhole geometry is locally indistinguishable from a cosmic string background, the corresponding selfforces are different even at the qualitative level. In fact in the cosmic string geometry the force is always repulsive while for the wormhole background we find that the force may point outwards or towards the wormhole throat depending on the parameters of the configuration. These results suggest that the study of the electromagnetic fields of charged particles is a useful tool for testing the global properties of a given background. *

Effect of a cylindrical thin-shell of matter on the electrostatic self-force on a charge

“…The procedure can be applied to interpret self-forces in other space-times with shells, and the above result motivated the same analysis for wormhole space-times. We took a previous work on self-forces on a charge in locally flat cylindrical TSWH [22], and we calculated the total net effective charge of the shell and found an inverse proportional relation with the concavity of the throat: Q wh ∓ /q = −1/(κ wh r ± ). We may ask if similar results appear in other wormholes, or in spherical TSST, relating shell fields and the extrinsic curvature discontinuity.…”

“…The equivalent problems in the bulk where q is placed always admit a shell field sourced by some σ a with a net effective total charge, because beyond the throat there is another asymptotic region. Applying the equivalent problem interpretation for a test charge in a locally flat cylindrical TSWH with conical asymptotics (similar to those considered in [22]) we obtain Q wh…”

“…[17][18][19][20][21], have also been considered to evaluate the self-force problem. In [22] we showed that the non-trivial topology of locally flat wormholes contribute with an attractive force toward the throat.…”

Thin-shell wormholes from the regular Hayward black hole

“…Thus one can accept the dynamic EoS of the wormhole to be the same as the static EoS [49][50][51][52][53][54][55]. This assumption, therefore, implies that the EoS is uniquely determined by f (a) and a, described by (22) and (23), i.e.,…”

Counter-rotational effects on stability of $$2+1$$ 2 + 1 -dimensional thin-shell wormholes

“…Among the works on TSWs we see generalizations to higher [18][19][20] and lower [21][22][23] dimensions, and extensions to Lovelock gravity [24][25][26][27]. The theory has also been considered in cylindrical symmetry [28][29][30][31][32][33][34], dilaton theory [35], and so on. The common feature of all these extensions is that the bulk spacetimes are all static.…”