A Morse-theoretical analysis of gravitational lensing by a Kerr-Newman black hole

Abstract

Consider, in the domain of outer communication M+ of a Kerr-Newman black hole, a point p (observation event) and a timelike curve γ (worldline of light source). Assume that γ (i) has no past end-point, (ii) does not intersect the caustic of the past light-cone of p, and (iii) goes neither to the horizon nor to infinity in the past. We prove that then for infinitely many positive integers k there is a past-pointing lightlike geodesic λ k of (Morse) index k from p to γ, hence an observer at p sees infinitely many images of γ. Moreover, we demonstrate that all lightlike geodesics from an event to a timelike curve in M+ are confined to a certain spherical shell. Our characterization of this spherical shell shows that in the Kerr-Newman spacetime the occurrence of infinitely many images is intimately related to the occurrence of centrifugal-plus-Coriolis force reversal.

Circular motion in NUT space-time

“…Hasse and Perlick [21] where this result was already found for the special case of the Kerr-Newman space-time. If g tφ = 0 we have of course R ± =R = R and a Cor + a cen = a cen is perpendicular to the surfaces R = constant for any v. In the NUT space-time the potential R ± is given by…”

“…In particular, the coordinates r in and θ in of the inner edge are related by (21). It is then equivalent for the toroidal configuration to use instead of the parameters and W in the two radii r cen and r in .…”

“…If K (r ms ) < < K (r mb ), the region with closed equipotential surfaces is bounded by an equipotential surface that forms a "cusp" at a radius coordinate r c which lies between r hor and r cen . The θ coordinates of the centre and of the cusp are to be determined by inserting r cen and r c , respectively, into (21). The choice of a value for W in defines the size of the configuration and whether or not it has an inner edge, see [23] and [17] for more details.…”

Chaotic lensing around boson stars and Kerr black holes with scalar hair

“…1. Chaotic scattering in GR spacetimes has been observed and discussed in binary or multi-BH solutions (see, e.g., [45,46,[74][75][76][77][78][79][80][81][82][83][84]) and is well known in the context of manybody scattering in classical dynamics, for example, the scattering of charged particles off magnetic dipoles [85] and the three-body problem (see, e.g., [86]). KBHsSH or RBSs provide an example of chaos in geodesic motion on the background of a single compact object, which moreover solves a simple and well-defined matter model minimally coupled to GR.…”

Optical caustics of Kerr spacetime: The full structure

“…A crucial step in the comprehension of physics in such extreme environments is the complete understanding of the phenomenology related to the bending of photon trajectories caused by spacetime curvature. In order to get reliable predictions on any observables, it is necessary to keep in mind that a Kerr black hole acts as a very strong gravitational lens, generating an infinite number of images of the same source [4]. The total flux of a source close to a Kerr black hole, (such as the accretion disk itself [5,6], an isolated bright spot on it [7,8] or a star orbiting the black hole [9]) gets a significant contribution from the secondary image and from higher order images [6].…”