Multipole Hair of Schwarzschild-Tangherlini Black Holes

Abstract

We study the field of an electric point charge that is slowly lowered into an $n+1$ dimensional Schwarzschild-Tangherlini black hole. We find that if $n>3$, then countably infinite nonzero multipole moments manifest to observers outside the event horizon as the charge falls in. This suggests the final state of the black hole is not characterized by a Reissner-Nordström-Tangherlini geometry. Instead, for odd $n$, the final state either possesses a degenerate horizon, undergoes a discontinuous topological transformation during the infall of the charge, or both. For even $n$, the final state is not guaranteed to be asymptotically-flat.

arXiv comment11 pages; v2/v3: small revisions; accepted to JMP

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Cited by in corpus (4)

• Analyzing the effect of higher dimensions on the black hole silhouette, deflection angles, and PINN approximated quasinormal modes
• Bianchi IX geometry and the Einstein-Maxwell theory
• The electric field of a charge in the vicinity of a higher dimensional black hole
• Electric Multipole Fields of Higher-Dimensional Massive Bodies