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Hidden symmetries, null geodesics, and photon capture in the Sen black hole

Kenta Hioki^1,* and Umpei Miyamoto^2,†

¹Department of Physics, Waseda University, Okubo 3-4-1, Tokyo 169-8555, Japan
²Racah Institute of Physics, Hebrew University, Givat Ram, Jerusalem 91904, Israel

^*hioki@gravity.phys.waseda.ac.jp
^†umpei@phys.huji.ac.il

Phys. Rev. D 78, 044007 – Published 6 August, 2008

DOI: https://doi.org/10.1103/PhysRevD.78.044007

Abstract

Important classes of null geodesics and hidden symmetries in the Sen black hole are investigated. First, we obtain the principal null geodesics and circular photon orbits. Then, an irreducible rank-two Killing tensor and a conformal Killing tensor are derived, which represent the hidden symmetries. Analyzing the properties of Killing tensors, we clarify why the Hamilton-Jacobi and wave equations are separable in this spacetime. We also investigate the gravitational capture of photons by the Sen black hole and compare the result with those by the various charged/rotating black holes and naked singularities in the Kerr-Newman family. For these black holes and naked singularities, we show the capture regions in a two dimensional impact parameter space (or equivalently the “shadows” observed at infinity) to form a variety of shapes such as the disk, circle, dot, arc, and their combinations.

Article Text

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