Superradiant Instability and Backreaction of Massive Vector Fields around Kerr Black Holes (1704.04791v2)

Abstract: We study the growth and saturation of the superradiant instability of a complex, massive vector (Proca) field as it extracts energy and angular momentum from a spinning black hole, using numerical solutions of the full Einstein-Proca equations. We concentrate on a rapidly spinning black hole ($a=0.99$) and the dominant $m=1$ azimuthal mode of the Proca field, with real and imaginary components of the field chosen to yield an axisymmetric stress-energy tensor and, hence, spacetime. We find that in excess of $9\%$ of the black hole's mass can be transferred into the field. In all cases studied, the superradiant instability smoothly saturates when the black hole's horizon frequency decreases to match the frequency of the Proca cloud that spontaneously forms around the black hole.

• The paper demonstrates that a massive Proca field’s superradiant instability transfers over 9% of a Kerr black hole's mass.
• The study employs advanced nonlinear Einstein-Proca simulations with axisymmetric geometry to model the energy extraction process.
• The results confirm Proca cloud formation with stationary energy density, validating theoretical predictions and guiding future gravitational wave research.

Superradiant Instability and Backreaction of Massive Vector Fields around Kerr Black Holes: An Analysis

The paper "Superradiant Instability and Backreaction of Massive Vector Fields around Kerr Black Holes," authored by William E. East and Frans Pretorius, presents a rigorous numerical paper on the nonlinear dynamics of massive vector field perturbations around rapidly spinning Kerr black holes. Specifically, the research explores the superradiant instability of a massive Proca field, characterized by its vector nature, which distinguishes it from the extensively studied scalar field cases.

Summary of Key Findings

The authors choose a scenario where the dimensionless spin parameter $a = 0.99$ for the black hole and focus on the fundamental $m=1$ azimuthal mode of the Proca field. The initial conditions are crafted such that the stress-energy tensor remains axisymmetric, simplifying the numerical depiction of spacetime.

1. Energy Transfer: The paper finds that more than $9\%$ of the black hole's mass can be effectively transferred to the Proca field. This transfer is dictated by the reduction of the black hole's horizon frequency, which adiabatically matches the wave frequency of the Proca cloud when the instability saturates.
2. Efficiency of Instability: The Proca field instability witnessed exponential growth due to the phase of superradiant extraction. Upon saturation, this energy extraction halts smoothly, with no overshoot phenomena like those suggested in previous studies involving other types of black holes.
3. Proca Cloud Formation: After saturation, a substantial Proca cloud forms around the black hole with energy and angular momentum properties that match theoretical predictions, including stationary energy density. Notably, the Proca field structure remains stable over the simulated time scale, forming a massive cloud around the black hole.
4. Effect on Black Hole: Analysis of the energy and angular momentum loss from the black hole shows an excellent match with theoretical assumptions, indicating the changes are primarily due to the field's growth rather than gravitational wave emissions.

Methodology and Numerical Approach

The paper employs a sophisticated numerical setup utilizing the full Einstein-Proca equations. The use of an axisymmetric spacetime geometry allows solving this problem within a two-dimensional computational domain, making the extensive time evolution feasible. The precision of the results is ensured by performing convergence tests and employing various resolutions to confirm robustness across computational expense scales.

Theoretical and Practical Implications

The findings have substantial implications in both theoretical physics and astrophysics. Theoretically, these results contribute to our understanding of superradiant instabilities in complex quantum field frameworks, providing a precedent for implications in the paper of bosonic fields related to dark matter candidates such as axions and dark photons. Practically, the extraction of angular momentum and energy through this mechanism may influence the evolutionary pathways of astrophysical black holes.

This paper sets a foundation for further explorations of higher azimuthal modes and their respective growth rates in spinning black holes. Furthermore, if the Proca clouds found are indeed stable, new directions in observing gravitational wave signatures may arise. The ongoing gravitational wave observations by facilities like LIGO hold the potential for testing these theoretical predictions by revealing deviations in black hole rotation rates in merging binaries.

Future Directions

The authors acknowledge the necessity of expanding this research to include a broader spectrum of modes, especially considering the slower growth rates of higher azimuthal modes. Such studies could unveil additional details regarding energy extraction limits and nonlinear growth behavior in this critical area of paper. Additionally, exploring the behavior of real Proca fields, compared to the complex field leads in this paper, may yield richer details about potential electromagnetic and gravitational radiation from these systems.

In conclusion, the research delivers a nuanced and comprehensive analysis of the superradiant instability for vector fields around Kerr black holes, significantly enhancing our understanding of this astrophysical phenomenon and opening new avenues for future investigations.