Quasinormal Modes of Rotating Black Holes and New Solitons in 5D Einstein-Gauss-Bonnet Gravity at the Chern-Simons Point

Kernkonzepte

This research paper presents new exact solutions for rotating black holes and static solitons in five-dimensional Einstein-Gauss-Bonnet gravity at the Chern-Simons point, analyzes the behavior of massless scalar probes on these backgrounds, and explores the impact of non-vanishing torsion.

Zusammenfassung

• Bibliographic Information: Tapia, L., Aguayo, M., Anabalón, A., Astefanesei, D., Grandi, N., Izaurieta, F., ... & Quinzacara, C. (2024). (Quasi-) normal modes of rotating black holes and new solitons in Einstein-Gauss-Bonnet. arXiv preprint arXiv:2411.08001.
• Research Objective: This study aims to construct new rotating black hole and static soliton solutions in 5D Einstein-Gauss-Bonnet gravity at the Chern-Simons point and investigate the propagation of massless scalar probes on these backgrounds. Additionally, the research explores the possibility of incorporating non-vanishing torsion into these solutions.
• Methodology: The authors employ a combination of analytical and numerical techniques. They derive new solutions by starting with a three-dimensional rotating, Kerr-Schild seed and oxidizing it to five dimensions using appropriate warp factors. The resulting geometries are analyzed for their asymptotic behavior and regularity. The propagation of massless scalar probes is studied by solving the Klein-Gordon equation on these backgrounds, employing separation of variables and numerical methods to determine the quasinormal mode frequencies. The possibility of incorporating torsion is investigated within the framework of Einstein-Cartan geometry.
• Key Findings: The research presents three new solutions to Einstein-Gauss-Bonnet theory at the Chern-Simons point: one describing a new rotating black hole and two corresponding to smooth gravitational solitons. Despite the non-compact nature of the extra dimensions, the scalar field exhibits a gapped, discrete Kaluza-Klein mass spectrum. The study reveals that co-rotating scalar modes on the rotating black holes have longer lifetimes than counter-rotating modes, with the imaginary part of the frequencies approaching zero as the black hole approaches extremality. Additionally, the research demonstrates that both the rotating black holes and solitons can accommodate non-vanishing, gravitating torsion, leading to a novel branch of solutions.
• Main Conclusions: The study significantly expands the known solutions in 5D Einstein-Gauss-Bonnet gravity at the Chern-Simons point by introducing new rotating black hole and soliton solutions. The analysis of scalar probe propagation reveals intriguing features, such as the distinct behavior of co- and counter-rotating modes and the emergence of a discrete mass spectrum. The incorporation of torsion opens up new avenues for exploring the properties and implications of these solutions.
• Significance: This research contributes significantly to the understanding of higher-dimensional gravity theories, particularly in the context of the AdS/CFT correspondence. The new solutions and their properties provide valuable insights into black hole physics, soliton dynamics, and the potential role of torsion in gravitational theories.
• Limitations and Future Research: The study primarily focuses on massless scalar probes. Investigating the behavior of other types of probes, such as fermions or higher-spin fields, could reveal further insights into the properties of these geometries. Additionally, exploring the implications of these solutions within the AdS/CFT correspondence and their potential connections to condensed matter physics could be fruitful avenues for future research.

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Wichtige Erkenntnisse aus

(Quasi-)normal modes of rotating black holes and new solitons in Einstein-Gauss-Bonnet

by Lili... um arxiv.org 11-13-2024

https://arxiv.org/pdf/2411.08001.pdf

Tiefere Fragen

How would the inclusion of matter fields, such as a scalar field with self-interactions, affect the stability and properties of these new black hole and soliton solutions?

Answer:
The inclusion of matter fields, especially self-interacting scalar fields, can significantly impact the stability and properties of the Einstein-Gauss-Bonnet black hole and soliton solutions. Here's how:

Stability:

New Instabilities: Self-interacting scalar fields can introduce new instability channels. For instance, the scalar field's energy density could accumulate near the horizon, potentially leading to a non-linear instability and altering the black hole's properties or even destroying the soliton altogether.
Modifying Existing Instabilities: The presence of matter can also modify the existing instabilities associated with black holes, such as superradiance. The scalar field could interact with the rotating black hole, either amplifying or damping the superradiant modes, thereby affecting the timescale of the instability.

Properties:

Backreaction on Geometry: The energy-momentum tensor of the matter field would contribute to the Einstein-Gauss-Bonnet field equations, leading to a backreaction on the spacetime geometry. This backreaction could modify the black hole's mass, angular momentum, and even the structure of the horizon. For solitons, this could alter their size, shape, and stability.
Hairy Black Holes and Solitons: Self-interacting scalar fields can give rise to "hairy" black hole solutions, where the scalar field does not vanish at the horizon. Similarly, hairy solitons could emerge, characterized by non-trivial scalar field profiles. These hairy solutions would possess distinct properties compared to their bald counterparts.
Investigating these effects would require studying the coupled system of Einstein-Gauss-Bonnet gravity and the self-interacting scalar field equations. Numerical analysis would likely be necessary to solve these coupled equations and determine the stability and properties of the resulting solutions.

Could the non-trivial asymptotic behavior of the new rotating black hole solution (6) be related to a different holographic dual compared to the asymptotically AdS solution (4)?

Answer:
Yes, the non-trivial asymptotic behavior of the new rotating black hole solution (6), which deviates from standard AdS asymptotics, strongly suggests a different holographic dual compared to the asymptotically AdS solution (4). Here's why:

AdS/CFT Correspondence and Asymptotics: The AdS/CFT correspondence relies heavily on the asymptotic structure of the bulk spacetime. The conformal boundary of AdS spacetime plays a crucial role in defining the dual conformal field theory (CFT). The symmetries of the asymptotic AdS spacetime are reflected in the conformal symmetries of the dual CFT.

Non-AdS Asymptotics and Holography: When a spacetime deviates from AdS asymptotics, the standard AdS/CFT dictionary may not directly apply. The non-trivial asymptotic behavior could indicate:

Modified Symmetries: The asymptotic symmetry group of solution (6) might differ from the conformal group SO(4,2) of AdS5. This suggests that the dual field theory, if it exists, would not be a standard CFT. It could be a different type of quantum field theory with symmetries reflecting the modified asymptotic symmetry group.
Non-Conformal Dual: The dual theory might not even be conformal. The non-AdS asymptotics could imply a different scaling behavior in the dual field theory, leading to a non-conformal theory.
Exploring the holographic dual of solution (6) would require carefully analyzing its asymptotic symmetry group and developing a modified holographic dictionary. This could involve identifying the relevant boundary conditions for fields in the bulk and understanding how they relate to operators in the dual theory.

What are the implications of the observed discrete mass spectrum for the scalar field in the context of the AdS/CFT correspondence, and could it be interpreted in terms of a dual conformal field theory?

Answer:
The observed discrete mass spectrum for the scalar field in these Einstein-Gauss-Bonnet backgrounds has intriguing implications for the AdS/CFT correspondence:

Dual Operators and Conformal Dimensions: In AdS/CFT, the masses of bulk fields correspond to the conformal dimensions of operators in the dual CFT. A discrete mass spectrum for the scalar field implies a discrete spectrum of conformal dimensions for the corresponding operators in the dual theory.

Kaluza-Klein Tower and CFT Interpretation: The discrete mass spectrum arises from the effective compactification of the ρ direction due to the spacetime's curvature, even though it's geometrically non-compact. This is analogous to a Kaluza-Klein tower of states. In the dual CFT, this could be interpreted as:

States in a Confining Potential: The discrete spectrum might indicate that the dual CFT lives in a space with a confining potential along a certain direction. The scalar field modes would correspond to bound states in this potential, leading to quantized energy levels and hence discrete conformal dimensions.
Discrete Spectrum of a Composite Operator: Alternatively, the discrete spectrum could represent the allowed conformal dimensions of a composite operator in the CFT. The scalar field in the bulk could be dual to a bound state of fundamental fields in the CFT, and the discrete mass spectrum would reflect the allowed energy levels of this bound state.

Gapped Spectrum and Implications: The fact that the mass spectrum is gapped (i.e., there's a minimum non-zero mass) suggests that the dual CFT has a mass gap. This means there's a finite energy difference between the ground state and the first excited state of the theory. This could have implications for the low-energy dynamics and phase structure of the dual CFT.
In summary, the discrete mass spectrum provides valuable information about the operator content and dynamics of the dual CFT. It suggests a theory with a discrete spectrum of conformal dimensions, possibly arising from a confining potential or a composite operator. The gapped nature of the spectrum further points to a mass gap in the dual CFT.