The second order quasi-normal modes for an AdS$_4$ black brane

Table of Contents

1. Summary
2. Highlights
3. Key Insights
4. Mindmap
5. Citation

Summary

The second-order quasi-normal modes for an AdS black brane are studied, with a focus on the gravitational perturbations. The equations of motion for the second-order modes are obtained, and the ratio of amplitudes between the second-order mode and the product of two linear modes in the source is numerically computed.

Highlights

• The second-order quasi-normal modes for an AdS black brane are sourced by two first-order quasi-normal modes.
• The ratio of amplitudes between the second-order mode and the product of two linear modes in the source is numerically computed.
• The quadratic-to-linear ratio of amplitudes at the horizon is found to be of order one in general.
• Resonance occurs at special positions in momentum space, where the amplitude becomes divergent.
• The condition leading to the resonance is that the combined frequency of two sources coincides with one of another first-order quasi-normal mode.
• The phenomenon is in contrast to what is observed in asymptotically flat spacetime.
• The quadratic-to-linear amplitudes of quasi-normal modes in asymptotically flat black holes have been studied in previous research.

Key Insights

• The study of second-order quasi-normal modes for an AdS black brane provides valuable insights into the gravitational perturbations and the behavior of black holes in AdS spacetime.
• The ratio of amplitudes between the second-order mode and the product of two linear modes in the source is a crucial quantity that characterizes the non-linear effects of gravity.
• The resonance phenomenon observed in the study is a unique feature of AdS black branes, which distinguishes them from asymptotically flat black holes.
• The condition leading to the resonance provides a new perspective on the behavior of quasi-normal modes and their interactions.
• The study of quadratic-to-linear amplitudes of quasi-normal modes has significant implications for our understanding of black hole physics and the AdS/CFT correspondence.
• The numerical computation of the ratio of amplitudes is a complex task that requires advanced computational techniques and a deep understanding of the underlying physics.
• The results of the study have the potential to shed new light on the non-linear effects of gravity and the behavior of black holes in AdS spacetime.

Mindmap

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Citation

Pan, W.-B., Yu, Z., & Ling, Y. (2024). The second order quasi-normal modes for an AdS${}_4$ black brane (Version 1). arXiv. https://doi.org/10.48550/ARXIV.2412.20683