Singular lensing from the scattering on special space-time defects

TL;DR

This paper investigates the resonant scattering and singular lensing effects caused by special space-time defects like global monopoles, addressing computational subtleties and regularization to clarify the phenomenon's physical validity.

Contribution

It introduces a regularization method for the scattering amplitudes on defect space-times, ensuring physical consistency and clarifying the conditions for singular lensing.

Findings

Regularization removes the lensing in the no-defect limit.

Confirms the singular lensing phenomenon through alternative calculations.

Ensures the optical theorem holds in the regularized framework.

Abstract

It is well known that certain special classes of self-gravitating point-like defects, such as global (non gauged) monopoles, give rise to non-asymptotically flat space-times characterized by solid angle deficits, whose size depends on the details of the underlying microscopic models. The scattering of electrically neutral particles on such space-times is described by amplitudes that exhibit resonant behaviour when the scattering and deficit angles coincide. This, in turn, leads to ring-like structures where the cross sections are formally divergent ("singular lensing"). In this work, we revisit this particular phenomenon, with the twofold purpose of placing it in a contemporary and more general context, in view of renewed interest in the theory and general phenomenology of such defects, and, more importantly, of addressing certain subtleties that appear in the particular computation that leads to the aforementioned effect. In particular, by adopting a specific regularization procedure for the formally infinite Legendre series encountered, we manage to ensure the recovery of the Minkowski space-time, and thus the disappearance of the lensing phenomenon, in the no-defect limit, and the validity of the optical theorem for the elastic total cross section. In addition, the singular nature of the phenomenon is confirmed by means of an alternative calculation, which, unlike the original approach, makes no use of the generating function of the Legendre polynomials, but rather exploits the asymptotic properties of the Fresnel integrals.