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 $d\ge 4$. 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 $T^1{S}^{n-1}\times {\mathbb{R}}^2$, as suggested in [7].

arXiv comment6 pages, comments welcome

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Cited by in corpus (5)

• Classification of static asymptotically flat spacetimes with a photon sphere in Einstein-multiple-scalar field theory
• Uniqueness of photon sphere for Reissner-Nordström electric-magnetic system
• Higher-dimensional electric-magnetic photon sphere uniqueness
• Charged Particles Capture Cross-Section by a Weakly Charged Schwarzschild Black Hole
• Uniqueness of electric-magnetic spacetimes with massive particle