Trapped photons in Schwarzschild-Tangherlini spacetimes

Abstract

We study the set of trapped photons outside the event horizon of Schwarzschild-Tangherlini black holes in dimension d≥4. We prove that the only trapped photons are those with constant Boyer-Lindquist coordinate radius.

We then identify the set of trapped photons as a submanifold of the tangent bundle of the spacetime, and prove that this submanifold has topology T1Sn-1 ×ℝ2, as suggested by Cederbaum-Jahns.

Keywords

• black-holes
• photon-region
• photonsphere
• Schwarzschild
• Schwarzschild Tangherlini