Feeding a Kerr black hole with quantized vortices

Abstract

By solving a nonlinear Klein-Gordon equation in Kerr geometry, we uncover new phenomena and key characteristics of quantized vortices in quantum fluids near a Kerr black hole. The formation of these vortices induces rotational or turbulent flows, which profoundly alter the fluid properties and revise those dark matter models describing axion condensates, ultralight boson clouds, and other scalar fields in the vicinity of spinning black holes. As macroscopic, quantum, and topological defects, these vortices can stably orbit the black hole over extended periods, establishing their viability as novel probes for investigating black hole physics. For instance, we calculate the angular velocities of orbiting vortices to quantitatively characterize the frame-dragging effect, a classic prediction of general relativity. Additionally, we observe that relatively large vortices are accreted onto the black hole, wrapping around it while undergoing splitting and reconnecting processes. In quantum fluids with high vortex densities, turbulent flows emerge, accompanied by the formation of a vortex boundary layer near the event horizon. Beyond the ergosphere, we find vortex emissions and energetic outbursts, which may provide crucial insights into analogous astrophysical events recently discovered by the XRISM satellite.

Figures (6)

• Figure 1: Density plots of $|\Phi|^2$ at the equatorial plane. $\delta \equiv 1- a = 10^{-7}, \lambda=0.1$. The static limit of the ergosphere is indicated by the red circles. (a) and (b): direct rotation -- the fluid follows the rotation of the black hole (counter-clockwise) when spiralling to the event horizon; (c) and (d): retrograde rotation -- the fluid rotates clockwise initially, and then splits into two parts rotating in opposite directions when entering the ergosphere.
• Figure 2: Quantized vortices orbiting around a Kerr black hole. The event horizons are indicated by the grey surfaces in (a-c, e) and the white circles in (d), respectively. (a) An illustration for a Kerr black hole: the ergoshpere is the region enclosed by the grey and brown surfaces; (b) Three cases with increasing rotational velocities of the black hole which correspond to $\delta = 10^{-2}, 10^{-3}$ and $10^{-7}$, respectively ($\lambda=0.1$); (c) Six vortices around the black hole; (d) Density (left) and phase (right) plots of $\Phi$ on the equatorial plane: Positions of each vortex intersecting with the equatorial plane are labelled by circles of the same color; (e) Three vortices orbit the black hole.
• Figure 3: The averaged angular velocities of three orbiting vortices (blue crosses) matches with the angular velocities of locally non-rotating observers (red line).
• Figure 4: Three relatively large vortices wind on the spinning black hole and reconnect to form a trefoil-like knot.
• Figure 5: Turbulent states in the ergosphere: (a) A vortex "lantern" with openings at the polar region of the black hole. The picture on the right, which visualizes more details of the turbulent flow, is connected to the left one by a coordinate transformation; (b) A histogram plot of the vorticity distribution inside the ergosphere: Initially located at the static limit, vortices advect toward the event horizon, forming a narrower and denser layer there.