Abstract
We propose and demonstrate a new and efficient approach to investigate black hole dynamics in the limit of large number of dimensions D. The basic idea is that an asymptotically flat black brane evolving under the Gregory-Laflamme instability forms lumps that closely resemble a localized black hole. In this manner, the large-D effective equations for extended black branes can be used to study localized black holes. We show that these equations have exact solutions for black-hole-like lumps on the brane, which correctly capture the main properties of Schwarzschild and Myers-Perry black holes at large D, including their slow quasinormal modes and the ultraspinning instabilities (axisymmetric or not) at large angular momenta. Furthermore, we obtain a novel class of rotating ‘black bar’ solutions, which are stationary when D → ∞, and are long-lived when D is finite but large, since their gravitational wave emission is strongly suppressed. The leading large D approximation reproduces to per-cent level accuracy previous numerical calculations of the bar-mode growth rate in D = 6, 7.
Highlights
Recent advances have shown that many problems in black hole physics simplify in an efficient way when expanded in the inverse of the number D of spacetime dimensions [1]–[47]
We propose and demonstrate a new and efficient approach to investigate black hole dynamics in the limit of large number of dimensions D
The large-D effective equations for extended black branes can be used to study localized black holes. We show that these equations have exact solutions for black-hole-like lumps on the brane, which correctly capture the main properties of Schwarzschild and Myers-Perry black holes at large D, including their slow quasinormal modes and the ultraspinning instabilities at large angular momenta
Summary
Recent advances have shown that many problems in black hole physics simplify in an efficient way when expanded in the inverse of the number D of spacetime dimensions [1]–[47]. The studies of linearized perturbations in [8] (greatly aided by the numerical work of [7]) revealed that the low frequency modes near the horizon of a black hole decouple, at all perturbation orders in 1/D, from the faster oscillations that propagate away from the horizon This has enabled the formulation of effective non-linear theories for the slow fluctuations of the black hole, which have been derived and put to use in several contexts. We will show that there is a simple, exact solution of the effective black brane equations that describes a bulge with many of the physical properties of a Schwarzschild black hole. In the large-D approximation, the bulge on the brane is a good approximation for only a ‘cap’ of the Schwarzschild (or Myers-Perry) black hole horizon√. Appendix C discusses the behavior at large radius of the solutions to our equations, and issues of existence beyond linear perturbation theory
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