The canonical ensemble reloaded: the complex-stability of Euclidean quantum gravity for black holes in a box
Abstract We revisit the stability of black hole saddles for the Euclidean path integral describing the canonical partition function Z(β) for gravity inside a spherical reflecting cavity. The boundary condition at the cavity wall couples the transverse-traceless (TT) and pure-trace modes that are tra...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-08-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP08(2022)215 |
| _version_ | 1818082173311254528 |
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| author | Donald Marolf Jorge E. Santos |
| author_facet | Donald Marolf Jorge E. Santos |
| author_sort | Donald Marolf |
| collection | DOAJ |
| description | Abstract We revisit the stability of black hole saddles for the Euclidean path integral describing the canonical partition function Z(β) for gravity inside a spherical reflecting cavity. The boundary condition at the cavity wall couples the transverse-traceless (TT) and pure-trace modes that are traditionally used to describe fluctuations about Euclidean Schwarzschild black holes in infinite-volume asymptotically flat and asymototically AdS spacetimes. This coupling obstructs the familiar Gibbons-Hawking-Perry treatment of the conformal factor problem, as Wick rotation of the pure-trace modes would require that the TT modes be rotated as well. The coupling also leads to complex eigenvalues for the Lichnerowicz operator. We nevertheless find that the Lichnerowicz operator can be diagonalized in the space of coupled modes. This observation allows the eigenmodes to define a natural generalization of the pure-trace Wick-rotation recipe used in infinite volume, with the result that a mode with eigenvalue λ is stable when Re λ > 0. In any cavity, and with any cosmological constant Λ ≤ 0, we show this recipe to reproduce the expectation from black hole thermodynamics that large Euclidean black holes define stable saddles while the saddles defined by small Euclidean black holes are unstable. |
| first_indexed | 2024-12-10T19:17:53Z |
| format | Article |
| id | doaj.art-228065a68a4e47c49fe584bfc02e88ca |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-10T19:17:53Z |
| publishDate | 2022-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-228065a68a4e47c49fe584bfc02e88ca2022-12-22T01:36:32ZengSpringerOpenJournal of High Energy Physics1029-84792022-08-012022813010.1007/JHEP08(2022)215The canonical ensemble reloaded: the complex-stability of Euclidean quantum gravity for black holes in a boxDonald Marolf0Jorge E. Santos1Department of Physics, University of California at Santa BarbaraDepartment of Applied Mathematics and Theoretical Physics, University of CambridgeAbstract We revisit the stability of black hole saddles for the Euclidean path integral describing the canonical partition function Z(β) for gravity inside a spherical reflecting cavity. The boundary condition at the cavity wall couples the transverse-traceless (TT) and pure-trace modes that are traditionally used to describe fluctuations about Euclidean Schwarzschild black holes in infinite-volume asymptotically flat and asymototically AdS spacetimes. This coupling obstructs the familiar Gibbons-Hawking-Perry treatment of the conformal factor problem, as Wick rotation of the pure-trace modes would require that the TT modes be rotated as well. The coupling also leads to complex eigenvalues for the Lichnerowicz operator. We nevertheless find that the Lichnerowicz operator can be diagonalized in the space of coupled modes. This observation allows the eigenmodes to define a natural generalization of the pure-trace Wick-rotation recipe used in infinite volume, with the result that a mode with eigenvalue λ is stable when Re λ > 0. In any cavity, and with any cosmological constant Λ ≤ 0, we show this recipe to reproduce the expectation from black hole thermodynamics that large Euclidean black holes define stable saddles while the saddles defined by small Euclidean black holes are unstable.https://doi.org/10.1007/JHEP08(2022)215AdS-CFT CorrespondenceBlack Holes in String TheoryGauge-Gravity Correspondence |
| spellingShingle | Donald Marolf Jorge E. Santos The canonical ensemble reloaded: the complex-stability of Euclidean quantum gravity for black holes in a box Journal of High Energy Physics AdS-CFT Correspondence Black Holes in String Theory Gauge-Gravity Correspondence |
| title | The canonical ensemble reloaded: the complex-stability of Euclidean quantum gravity for black holes in a box |
| title_full | The canonical ensemble reloaded: the complex-stability of Euclidean quantum gravity for black holes in a box |
| title_fullStr | The canonical ensemble reloaded: the complex-stability of Euclidean quantum gravity for black holes in a box |
| title_full_unstemmed | The canonical ensemble reloaded: the complex-stability of Euclidean quantum gravity for black holes in a box |
| title_short | The canonical ensemble reloaded: the complex-stability of Euclidean quantum gravity for black holes in a box |
| title_sort | canonical ensemble reloaded the complex stability of euclidean quantum gravity for black holes in a box |
| topic | AdS-CFT Correspondence Black Holes in String Theory Gauge-Gravity Correspondence |
| url | https://doi.org/10.1007/JHEP08(2022)215 |
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