Quantum time uncertainty in Schwarzschild-anti-de Sitter black holes
| dc.contributor.author | Galan, Pablo | |
| dc.contributor.author | Garay Elizondo, Luis Javier | |
| dc.contributor.author | Mena Marugán, Guillermo A. | |
| dc.date.accessioned | 2023-06-20T10:51:34Z | |
| dc.date.available | 2023-06-20T10:51:34Z | |
| dc.date.issued | 2007-08 | |
| dc.description | © 2007 The American Physical Society. The authors want to thank V. Aldaya and C. Barceló for fruitful conversations and enlightening discussions. P. G. is also very thankful to F. Barbero and J. M. Martín-García for their valuable help. P. G. gratefully acknowledges the financial support provided by the I3P framework of CSIC and the European Social Fund. This work was supported by funds provided by the Spanish MEC Projects No. FIS2005-05736-C03-02 and No. FIS2006-26387-E. | |
| dc.description.abstract | The combined action of gravity and quantum mechanics gives rise to a minimum time uncertainty in the lowest order approximation of a perturbative scheme, in which quantum effects are regarded as corrections to the classical spacetime geometry. From the nonperturbative point of view, both gravity and quantum mechanics are treated on equal footing in a description that already contains all possible backreaction effects as those above in a nonlinear manner. In this paper, the existence or not of such minimum time uncertainty is analyzed in the context of Schwarzschild-anti-de Sitter black holes using the isolated horizon formalism. We show that from a perturbative point of view, a nonzero time uncertainty is generically present owing to the energy scale introduced by the cosmological constant, while in a quantization scheme that includes nonperturbatively the effects of that scale, an arbitrarily high time resolution can be reached. | |
| dc.description.department | Depto. de Física Teórica | |
| dc.description.faculty | Fac. de Ciencias Físicas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Spanish MEC Projects | |
| dc.description.sponsorship | CSIC | |
| dc.description.sponsorship | European Social Fund | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/29819 | |
| dc.identifier.doi | 10.1103/PhysRevD.76.044014 | |
| dc.identifier.issn | 1550-7998 | |
| dc.identifier.officialurl | http://dx.doi.org/10.1103/PhysRevD.76.044014 | |
| dc.identifier.relatedurl | http://journals.aps.org | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/51349 | |
| dc.issue.number | 4 | |
| dc.journal.title | Physical review D | |
| dc.language.iso | eng | |
| dc.publisher | Amer Physical Soc | |
| dc.relation.projectID | FIS2005-05736-C03-02 | |
| dc.relation.projectID | FIS2006-26387-E | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 51-73 | |
| dc.subject.keyword | Isolated horizons | |
| dc.subject.keyword | Space-time | |
| dc.subject.keyword | Gravity | |
| dc.subject.keyword | Symmetries | |
| dc.subject.keyword | Limits | |
| dc.subject.keyword | Area | |
| dc.subject.ucm | Física-Modelos matemáticos | |
| dc.subject.ucm | Física matemática | |
| dc.title | Quantum time uncertainty in Schwarzschild-anti-de Sitter black holes | |
| dc.type | journal article | |
| dc.volume.number | 76 | |
| dcterms.references | [1] L. J. Garay, Int. J. Mod. Phys. A 10, 145 (1995); and references therein. [2] T. Padmanabhan, Classical Quantum Gravity 4, L107 (1987). [3] G. Amelino-Camelia, Mod. Phys. Lett. A 9, 3415 (1994); 11, 1411 (1996); 13, 1319 (1998). [4] G. Amelino-Camelia, Phys. Rev. D 62, 024015 (2000); Y. J. Ng and H. van Dam, Found. Phys. 30, 795 (2000). [5] J. F. Barbero G., G. A. Mena Marugán, and E. J. S. Villaseñoor, Phys. Rev. D 69, 044017 (2004). [6] P. Galán and G. A. Mena Maruga´n, Phys. Rev. D 70, 124003 (2004). [7] P. Galán and G. A. Mena Marugán, Phys. Rev. D 72, 044019 (2005). [8] C. Rovelli and L. Smolin, Nucl. Phys. B442, 593 (1995); B456, 753 (1995); A. Ashtekar and J. Lewandowski, Classical Quantum Gravity 14, A55 (1997). [9] S. Lloyd, Nature (London) 406, 1047 (2000). [10] Y. J. Ng, Mod. Phys. Lett. A 18, 1073 (2003); arXiv:gr-qc/ 0401015; Y. J. Ng and H. van Dam, Int. J. Mod. Phys. A 20, 1328 (2005). [11] R. M. Wald, General Relativity (Chicago Press, Chicago, 1984). [12] A. Ashtekar, A. Corichi, and K. Krasnov, Adv. Theor. Math. Phys. 3, 419 (2000); A. Ashtekar et al., Phys. Rev. Lett. 85, 3564 (2000); A. Ashtekar, C. Beetle, and S. Fairhurst, Classical Quantum Gravity 17, 253 (2000); A. Ashtekar, C. Beetle, and J. Lewandowski, Phys. Rev. D 64, 044016 (2001). [13] A. Ashtekar, S. Fairhurst, and B. Krishnan, Phys. Rev. D 62, 104025 (2000). [14] We adopt units in which @ c G 1, with @ being Planck constant, G Newton constant, and c the speed of light. [15] M. Henneaux and C. Teitelboim, Commun. Math. Phys. 98, 391 (1985); J. D. Brown and M. Henneaux, Commun. Math. Phys. 104, 207 (1986). [16] A. Corichi and A. Gomberoff, Phys. Rev. D 69, 064016 (2004). [17] A. Ashtekar and S. Das, Classical Quantum Gravity 17, L17 (2000). [18] A. Ashtekar, J. C. Baez, and K. Krasnov, Adv. Theor. QMath. Phys. 4, 1 (2000). [19] Some references where the quantization of the static Schwarzschild solutions is studied are J. Makela and P. Repo, Phys. Rev. D 57, 4899 (1998); J. Makela, P. Repo, M. Luomajoki, and J. Piilonen, Phys. Rev. D 64, 024018 (2001); C. Vaz and L. Witten, Phys. Rev. D 60, 024009 (1999). [20] This implies a nonvanishing uncertainty in any physical time interval, since we have identified the zero time with the instant at which we start the measurement process. [21] We consider states with hM^ i < 1 and, if needed, take on them the limit M ! 0. [22] It suffices that there exists a positive constant C such that hM^ 2ni < Cn 8 n 1. [23] For this, we have assumed that the time T can be large and restricted ourselves to states with bounded expectation values hM^ 2ni as explained in [22]. [24] I. S. Gradshteyn and I. M. Ryzhik, in Table of Integrals, Series and Products, edited by A. Jeffrey and D. Zwillinger (Academic Press, San Diego, 2000), 6th ed. [25] C. M. Bender and S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers (Springer-Verlag, New York, 1999). | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 5638c18d-1c35-40d2-8b77-eb558c27585e | |
| relation.isAuthorOfPublication.latestForDiscovery | 5638c18d-1c35-40d2-8b77-eb558c27585e |
Download
Original bundle
1 - 1 of 1
