Local Group Velocity Distribution inside Superradiant Condensates

TL;DR

This paper investigates the velocity distribution within superradiant scalar condensates around rotating black holes, revealing complex radial, polar, and azimuthal velocity behaviors far from the black hole.

Contribution

It uncovers the nontrivial group velocity distribution in superradiant condensates, extending understanding beyond phase velocity to include radial and angular velocity components.

Findings

Radial velocity approaches $(r_g\mu/2) \sin(2\omega t - 2\varphi)$ far from BH

Polar and azimuthal velocities decline as $1/r$

Velocity distribution exhibits nontrivial group velocity behavior

Abstract

Superradiance enables scalar fields to extract energy and angular momentum from a rotating black hole (BH), leading to the formation of a BH-condensate system. Previous studies mainly focus on the phase velocity, which propagates in the azimuthal direction. In this work, we show that the superradiant scalar condensate presents a nontrivial group velocity distribution. In the region sufficiently far from the BH, the condensate exhibits a radial velocity magnitude that approaches $ (r_g\mu/2) \sin (2\omega t-2 \varphi)$, while the polar and azimuthal velocity magnitudes asymptotically decline as $\propto 1/r$.