Electric Multipole Fields of Higher-Dimensional Massive Bodies

Abstract

It was shown in a recent paper [J. Math. Phys. 60, 102502 (2019)] that slowly lowering an electric charge into a Schwarzschild-Tangherlini (ST) black hole endows the final state with electric multipole fields, which implies the final state geometry is not Reissner-Nordström-Tangherlini in nature. This conclusion departs from the four-dimensional case in which the no-hair theorem (NHT) requires the final state to be a Reissner-Nordström black hole. To better understand this discrepancy clearly requires a deeper understanding of the origin of the multipole hair in the higher-dimensional case. In this paper, we advance the conjecture that charged, static, and asymptotically-flat higher-dimensional black holes can acquire electric multipole hair only after they form. This supposition derives from studying the asymptotic behavior of the field of a multipole charge onto which a massive and hyperspherical shell with an exterior ST geometry is collapsing. In the mathematical limit as the shell approaches its ST radius, we find that the multipole fields (except the monopole) vanish. This implies that the only information of an arbitrary (but finite) charge distribution inside the collapsing shell that is available to an asymptotic observer is the total electric charge. Our results yield considerable insight into how higher-dimensional black holes acquire electric multipole hair, and also imply that, in four dimensions, the fadeaway of multipole moments during gravitational collapse is not strictly because of the NHT.

arXiv comment11 pages; updated references; accepted to PRD

References in corpus (21)

• The Large N Limit of Superconformal Field Theories and Supergravity
• Large N Field Theories, String Theory and Gravity
• A rotating black ring in five dimensions
• Black Holes in Higher Dimensions
• Stationary Black Holes: Uniqueness and Beyond
• A generalization of Hawking's black hole topology theorem to higher dimensions
• World-Volume Effective Theory for Higher-Dimensional Black Holes
• Uniqueness and non-uniqueness of static black holes in higher dimensions
• Uniqueness and non-uniqueness of static vacuum black holes in higher dimensions
• Uniqueness of (dilatonic) charged black holes and black p-branes in higher dimensions
• Uniqueness Theorem of Static Degenerate and Non-degenerate Charged Black Holes in Higher Dimensions
• On non-existence of static vacuum black holes with degenerate components of the event horizon
• The classification of static vacuum space-times containing an asymptotically flat spacelike hypersurface with compact interior
• Degenerate Stars and Gravitational Collapse in AdS/CFT
• Black hole uniqueness theorems in higher dimensional spacetimes
• Classification of Static Charged Black Holes in Higher Dimensions
• Holographic Neutron Stars
• On the Topology of Black Hole Event Horizons in Higher Dimensions
• Collapsing and static thin massive charged dust shells in a Reissner-Nordström black hole background in higher dimensions
• Topology and Uniqueness of Higher Dimensional Black Holes
• Multipole Hair of Schwarzschild-Tangherlini Black Holes