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Analytic Kerr black hole lensing for equatorial observers in the strong deflection limit

V. Bozza^1,2,3, F. De Luca^2,3,4, G. Scarpetta^2,3,5, and M. Sereno^3,6,7

¹Centro Studi e Ricerche “Enrico Fermi,” Compendio Viminale, I-00184, Rome, Italy
²Dipartimento di Fisica “E. R. Caianiello,” Università di Salerno, via Allende, I-84081 Baronissi (SA), Italy
³Istituto Nazionale di Fisica Nucleare, Sezione di Napoli, Italy
⁴Institut für Theoretische Physik der Universität Zürich, CH-8057 Zürich, Switzerland
⁵International Institute for Advanced Scientific Studies, Vietri sul Mare (SA), Italy
⁶Dipartimento di Scienze Fisiche, Università degli Studi di Napoli ‘Federico II’, Via Cinthia, Monte S. Angelo, 80126 Napoli, Italy
⁷Istituto Nazionale di Astrofisica, Osservatorio Astronomico di Capodimonte, Salita Moiariello, 16, 80131 Napoli, Italy

Phys. Rev. D 72, 083003 – Published 19 October, 2005

DOI: https://doi.org/10.1103/PhysRevD.72.083003

Abstract

In this paper we present an analytical treatment of gravitational lensing by Kerr black holes in the limit of very large deflection angles, restricting to observers in the equatorial plane. We accomplish our objective starting from the Schwarzschild black hole and adding corrections up to second order in the black hole spin. This is sufficient to provide a full description of all caustics and the inversion of lens mapping for sources near them. On the basis of these formulae we argue that relativistic images of low mass x-ray binaries around Sgr $A^{*}$ are very likely to be seen by future x-ray interferometry missions.

Article Text

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