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

TL;DR

This paper explores the null geodesics, hidden symmetries, and photon capture phenomena in the Sen black hole, revealing new insights into its geometric and physical properties compared to other black hole solutions.

Contribution

It derives the principal null geodesics, circular photon orbits, and hidden symmetries of the Sen black hole, and compares photon capture regions with other black holes and naked singularities.

Findings

Principal null geodesics and photon orbits identified

Hidden symmetries via Killing tensors derived

Photon capture regions vary in shape across different black holes

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.