Self-force on an arbitrarily coupled scalar charge in cylindrical thin-shell spacetimes

Abstract

We consider the arbitrarily coupled field and self-force of a static massless scalar charge in cylindrical spacetimes with one or two asymptotic regions, with the only matter content concentrated in a thin-shell characterized by the trace of the extrinsic curvature jump κ. The self-force is studied numerically and analytically in terms of the curvature coupling ξ. We found the critical values ξ (n) c = n/ (ρ(r s ) κ), with n ∈ N and ρ(r s ) the metric's profile function at the position of the shell, for which the scalar field is divergent in the background configuration. The pathological behavior is removed by restricting the coupling to a domain of stability. The coupling has a significant influence over the self-force at the vicinities of the shell, and we identified ξ = 1/4 as the value for which the scalar force changes sign at a neighborhood of r s ; if κ(1 − 4ξ) > 0 the shell acts repulsively as an effective potential barrier, while if κ(1 − 4ξ) < 0 it attracts the charge as a potential well. The sign of the asymptotic self-force only depends on whether there is an angle deficit or not on the external region where the charge is placed; conical asymptotics produce a leading attractive force, while Minkowski regions produce a repulsive asymptotic self-force. PACS number(s): 4.20. 04.20.Gz, 41.20.Cv

Arbitrarily coupled massive scalar field in conical thin-shell spacetimes

“…If m → 0 then ξ (0) c → 0, and the safety domain takes only positive values of ξ if κ < 0, or only negative values if κ > 0. This last result coincides with the critical couplings found on a previous work were we used a massless scalar field in conical backgrounds to test the self-force on a charged scalar particle [20]. Despite this, we note that in the mentioned article some part of the analysis was performed outside the safety domain.…”

“…Conversely, a positive ξ with negative κ contributes repulsively; a weakened attractive force is seen if ξ < 1/6, and a dominant repulsion from the shell is observed everywhere if ξ 1/4. The value ξ = 1/4 was identified in a previous work [20] as the coupling which cancels out the delta-like potential at the shell in the analogous problem (for the radial solutions) defined in terms of a wave function propagating in an effective potential. Figure 3b refers to a Type I spacetime with an exotic matter thin shell, κ > 0, of parameters ω i = 0.9, ω e = 1 and r i m = 1.…”

“…The analysis of Refs. [10,11] was recently extended [20] to address the problem of the self-force on a scalar point charge within the theory of a massless scalar field. Scalar fields are considered of interest in modern cosmology, both within the study of the early Universe and, after the first proposals relating the apparently necessary Λ term to a scalar field (see for instance Ref.…”

“…The study of Ref. [20] in cylindrical spacetimes was performed in terms of the coupling of a massless scalar field, and critical values of this constant for which the scalar field is unstable in the background configuration were identified. In addition, the aforementioned analogy proposed by Bezerra and Khusnutdinov was particularly useful in the latter work to understand the role of the coupling ξ = 1/4, which cancels out the delta-like effective potential at the shell in cylindrically symmetric spacetimes, and for which the self-force changes its sign at the vicinities of the shell.…”

Electrostatics and self-force in asymptotically flat cylindrical wormholes

“…We have then addressed the determination of the self-force in cylindrical thin-shell spacetimes [14,15] and also in spherically symmetric ones [16] or different number of spacetime dimensions [17]. Our program has also been extended to the case of scalar massless and massive fields [18,19].…”