Trapped photons in Schwarzschild-Tangherlini spacetimes

TL;DR

This paper characterizes the set of trapped photons outside Schwarzschild-Tangherlini black holes in higher dimensions, showing they are confined to constant radius and form a specific submanifold with a detailed topological structure.

Contribution

It proves that trapped photons are only those at constant radius and identifies their precise topological structure in higher-dimensional black hole spacetimes.

Findings

Trapped photons occur only at constant Boyer-Lindquist radius.

The set of trapped photons forms a submanifold with topology T^1 S^{n-1}× R^2.

The results extend understanding of photon trapping in higher-dimensional black holes.

Abstract

We study the set of trapped photons outside the event horizon of Schwarzschild-Tangherlini black holes in dimension $d\geq4$. 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 $T^1 S^{n-1}\times \mathbb{R}^2$, as suggested in [7].