Gravitational lensing in the strong field limit

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.

Time Delay in Black Hole Gravitational Lensing as a Distance Estimator

“…(15). Substituting all the expressions back into (31), we can check that it is equivalent to (28), but now it is written as a sum of separately convergent integrals.…”

“…By the characteristics of the first two relativistic images, we can get the coefficients a and b, according to the procedure described in [15]. They are generally sufficient to identify the class of the specific black hole.…”

“…Yet, as noted in [15], in order to achieve this, we need an optical resolution one or two orders of magnitude better than that reachable by short-term VLBI projects [22]. Therefore, relativistic images will possibly become a target for next generation projects.…”

“…We shall briefly recall the main steps of that derivation referring the reader to Refs. [15,17] for all the details.…”

“…A full generalization of the strong field limit for any spherically symmetric spacetime was drawn in Ref. [15] and applied to several black hole metrics, allowing a non-degenerate discrimination among different collapsed objects. In work [16], the method was used to examine the characteristics of a Gibbons-MaedaGarfinkle-Horowitz-Strominger charged black hole of heterotic string theory.…”