From entropy to echoes: Counting the quasi-normal modes and the quantum limit of silence
We estimate the canonical entropy of a quantum black hole by counting its quasi-normal modes. We first show that the partition function of a classical black hole, evaluated by counting the quasi-normal modes with a thermodynamic Boltzmann weight, leads to a small entropy of order unity due to the sm...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2023-06-01
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| Series: | Physics Letters B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0370269323002356 |
| _version_ | 1797822142567415808 |
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| author | Naritaka Oshita Niayesh Afshordi |
| author_facet | Naritaka Oshita Niayesh Afshordi |
| author_sort | Naritaka Oshita |
| collection | DOAJ |
| description | We estimate the canonical entropy of a quantum black hole by counting its quasi-normal modes. We first show that the partition function of a classical black hole, evaluated by counting the quasi-normal modes with a thermodynamic Boltzmann weight, leads to a small entropy of order unity due to the small contribution from higher angular modes. We then discuss how this will be modified when taking into account dissipation effects near the horizon due to interaction with the quantum black hole microstates. The structure of quasi-normal modes drastically changes, yielding a fundamental frequency of the inverse of techo∼ log(Entropy)/Temperature. This is the time-scale for reflection from the microstates (or the quantum time limit of silence, followed by echoes), independent of the strength of dissipation, and is comparable to the scrambling time proposed by Sekino & Susskind. Setting the dissipation constant to Planck time, we reproduce the Bekenstein-Hawking entropy of ∼ (Horizon area)/(Planck area). This result suggests the possibility of simulating black hole entropy in analog horizons realized in condensed matter systems. |
| first_indexed | 2024-03-13T10:03:33Z |
| format | Article |
| id | doaj.art-c2bad0221b16498882fccbf394061cc7 |
| institution | Directory Open Access Journal |
| issn | 0370-2693 |
| language | English |
| last_indexed | 2024-03-13T10:03:33Z |
| publishDate | 2023-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Physics Letters B |
| spelling | doaj.art-c2bad0221b16498882fccbf394061cc72023-05-23T04:20:42ZengElsevierPhysics Letters B0370-26932023-06-01841137901From entropy to echoes: Counting the quasi-normal modes and the quantum limit of silenceNaritaka Oshita0Niayesh Afshordi1RIKEN iTHEMS, Wako, Saitama, 351-0198, JapanDepartment of Physics and Astronomy, University of Waterloo, 200 University Ave W, N2L 3G1, Waterloo, Canada; Waterloo Centre for Astrophysics, University of Waterloo, Waterloo, ON, N2L 3G1, Canada; Perimeter Institute For Theoretical Physics, 31 Caroline St N, Waterloo, CanadaWe estimate the canonical entropy of a quantum black hole by counting its quasi-normal modes. We first show that the partition function of a classical black hole, evaluated by counting the quasi-normal modes with a thermodynamic Boltzmann weight, leads to a small entropy of order unity due to the small contribution from higher angular modes. We then discuss how this will be modified when taking into account dissipation effects near the horizon due to interaction with the quantum black hole microstates. The structure of quasi-normal modes drastically changes, yielding a fundamental frequency of the inverse of techo∼ log(Entropy)/Temperature. This is the time-scale for reflection from the microstates (or the quantum time limit of silence, followed by echoes), independent of the strength of dissipation, and is comparable to the scrambling time proposed by Sekino & Susskind. Setting the dissipation constant to Planck time, we reproduce the Bekenstein-Hawking entropy of ∼ (Horizon area)/(Planck area). This result suggests the possibility of simulating black hole entropy in analog horizons realized in condensed matter systems.http://www.sciencedirect.com/science/article/pii/S0370269323002356 |
| spellingShingle | Naritaka Oshita Niayesh Afshordi From entropy to echoes: Counting the quasi-normal modes and the quantum limit of silence Physics Letters B |
| title | From entropy to echoes: Counting the quasi-normal modes and the quantum limit of silence |
| title_full | From entropy to echoes: Counting the quasi-normal modes and the quantum limit of silence |
| title_fullStr | From entropy to echoes: Counting the quasi-normal modes and the quantum limit of silence |
| title_full_unstemmed | From entropy to echoes: Counting the quasi-normal modes and the quantum limit of silence |
| title_short | From entropy to echoes: Counting the quasi-normal modes and the quantum limit of silence |
| title_sort | from entropy to echoes counting the quasi normal modes and the quantum limit of silence |
| url | http://www.sciencedirect.com/science/article/pii/S0370269323002356 |
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