Gravitational lensing in the strong field limit

TL;DR

This paper develops an analytic approach to distinguish black holes by their strong field gravitational lensing signatures, applicable to various spherically symmetric spacetimes, and connects theoretical coefficients to observable lensing features.

Contribution

It introduces a generic formalism for analyzing strong field lensing in spherically symmetric spacetimes without relying on specific field equations.

Findings

Deflection angle diverges logarithmically near the photon capture radius.

Different black hole types have distinct strong field lensing coefficients.

Estimated observational requirements to detect relativistic images of the galactic center black hole.

Abstract

We provide an analytic method to discriminate among different types of black holes on the ground of their strong field gravitational lensing properties. We expand the deflection angle of the photon in the neighbourhood of complete capture, defining a strong field limit, in opposition to the standard weak field limit. This expansion is worked out for a completely generic spherically symmetric spacetime, without any reference to the field equations and just assuming that the light ray follows the geodesics equation. We prove that the deflection angle always diverges logarithmically when the minimum impact parameter is reached. We apply this general formalism to Schwarzschild, Reissner-Nordstrom and Janis-Newman-Winicour black holes. We then compare the coefficients characterizing these metrics and find that different collapsed objects are characterized by different strong field limits. The strong field limit coefficients are directly connected to the observables, such as the position and the magnification of the relativistic images. As a concrete example, we consider the black hole at the centre of our galaxy and estimate the optical resolution needed to investigate its strong field behaviour through its relativistic images.