Kerr black holes with scalar hair (1403.2757v3)

Abstract: We present a family of solutions of Einstein's gravity minimally coupled to a complex, massive scalar field, describing asymptotically flat, spinning black holes with scalar hair and a regular horizon. These hairy black holes (HBHs) are supported by rotation and have no static limit. Besides mass M and angular momentum J, they carry a conserved, continuous Noether charge Q measuring the scalar hair. HBHs branch off from the Kerr metric at the threshold of the superradiant instability and reduce to spinning boson stars in the limit of vanishing horizon area. They overlap with Kerr black holes for a set of (M,J) values. A single Killing vector field preserves the solutions, tangent to the null geodesic generators of the event horizon. HBHs can exhibit sharp physical differences when compared to the Kerr solution, such as J/M^2>1, quadrupole moment larger than J^2/M and larger orbital angular velocity at the innermost stable circular orbit. Families of HBHs connected to the Kerr geometry should exist in scalar (and other) models with more general self interactions.

• The paper demonstrates that Kerr black holes can host scalar hair characterized by a continuous Noether charge, thereby challenging traditional no-hair theorems.
• The paper employs both linearized analysis and nonlinear numerical methods to reveal that rotation sustains scalar hair only above the superradiant instability threshold.
• The paper bridges the gap between Kerr black holes and spinning boson stars, opening new avenues for exploring gravitational and quantum field interactions.

Insights into Kerr Black Holes with Scalar Hair

The paper "Kerr black holes with scalar hair" by Carlos A. R. Herdeiro and Eugen Radu presents an intriguing family of solutions within Einstein's gravity framework, wherein the traditional Kerr black holes are endowed with scalar hair. This paper extends the understanding of black hole solutions by incorporating a massive scalar field, challenging the conventional no-hair theorems and promoting new possibilities in theoretical astrophysics.

Conceptual Framework

The authors investigate the theoretical possibility of equipping the Kerr black holes with scalar "hair" through the lens of Einstein's gravity, minimally coupled with a complex, massive scalar field. These "hairy" black holes (HBHs) are characterized by a scalar field contributing additional properties that traditional Kerr black holes lack. The HBH solutions bridge Kerr black holes with spinning boson stars, presenting a continuum where scalar fields play a pivotal role.

Key Findings

1. Scalar Hair: HBHs possess a continuous Noether charge $Q$, attributed to the scalar field, augmenting their description beyond mass $M$ and angular momentum $J$. This introduces a novel parameter that quantifies the scalar hair attached to the black holes.
2. Nonstatic Nature: These solutions are maintained by rotation and cannot exist in a non-rotating (static) state. The deviation from the Kerr solutions occurs at the superradiant instability threshold, allowing these black holes to manifest distinctively from traditional predictions.
3. Stationary and Axially Symmetric Solutions: While preserving these symmetries, the solutions are invariant only under a single Killing vector field, outside the applicability of traditional no-hair theorems.
4. Superradiant Instability: The presence of the scalar field in stationary and axially symmetric configurations suggests that such matter fields could stabilize through superradiant instabilities.

Numerical and Analytical Insights

The authors employed both linearized analyses and nonlinear numerical solutions to explore the emergence of HBHs. The linear analysis predicts scalar clouds around Kerr black holes, indicating possible instability regions that signal the potential for scalar hair development. Nonlinear computations then confirm the existence of stable HBHs, delineating their parameter space in terms of ADM mass, angular momentum, and scalar charges.

Theoretical Implications

• Black Hole Physics: The paper challenges the uniqueness theorems of black holes by demonstrating hair within scalar field models. This not only enriches the existing black hole family but also suggests potential observational signatures distinguishing HBHs from traditional Kerr solutions.
• Astrophysical Relevance: Although the current astrophysical relevance is dependent on the scalar field mass, which may not be apparent according to current observational scales, it hints at unexplored particle physics phenomena potentializing such states.
• Interdisciplinary Connections: These HBHs offer a unique intersect between gravitational and quantum field theories, allowing insights into compact objects that might harbor rich physical interactions.

Future Directions

Future research may look into the explicit stability regimes of these solutions, particularly concerning superradiant instability effects, and may explore extensions to gauge theories or alternate geometries like Kerr-Newman or AdS configurations. Additionally, the paper of other field interactions could uncover more complex manifestations of hairy black holes, potentially unveiling new astrophysical observations.

In conclusion, this research opens avenues for deeper exploration into the gravitational effects of matter fields near black holes, challenging the traditional paradigms that have long stood in black hole physics and suggesting new fields of inquiry within astrophysical and theoretical physics landscapes.