Abstract
Photon spheres are the characteristic of general black holes, thus are a suitable touchstone for the emergence of gravitational spacetime in the AdS/CFT correspondence. We provide a spectral analysis of an AdS Schwarzschild black hole near its photon sphere. We find that quasinormal modes near the photon sphere reflect the AdS boundary, resulting in a peculiar spectral pattern. Our large angular momentum analysis owes to an analogue to solvable Schrödinger equations such as an inverted harmonic oscillator and the Pöschl-Teller model, with a Dirichlet boundary condition. Through the AdS/CFT dictionary, it predicts the existence of a peculiar subsector in the large angular momentum spectrum of thermal holographic CFTs on a sphere.
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Acknowledgments
We would like to thank K. Yoshida for valuable discussions. The work of K. H. was supported in part by JSPS KAKENHI Grant No. JP22H01217, JP22H05111 and JP22H05115. The work of K. S. was supported in part by Grant-in-Aid for JSPS Fellows No. 23KJ1310. The work of T. Y. was supported in part by JSPS KAKENHI Grant No. JP22H05115 and JP22KJ1896.
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Hashimoto, K., Sugiura, K., Sugiyama, K. et al. Photon sphere and quasinormal modes in AdS/CFT. J. High Energ. Phys. 2023, 149 (2023). https://doi.org/10.1007/JHEP10(2023)149
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DOI: https://doi.org/10.1007/JHEP10(2023)149