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Quantum time uncertainty in Schwarzschild–anti-de Sitter black holes

Pablo Galán^1,*, Luis J. Garay^2,1,†, and Guillermo A. Mena Marugán^1,‡

¹Instituto de Estructura de la Materia, CSIC, Serrano 121, 28006 Madrid, Spain
²Departamento de Física Teórica II, Universidad Complutense de Madrid, 28040 Madrid, Spain

^*galan@iem.cfmac.csic.es
^†luis.garay@fis.ucm.es
^‡mena@iem.cfmac.csic.es

Phys. Rev. D 76, 044014 – Published 17 August, 2007

DOI: https://doi.org/10.1103/PhysRevD.76.044014

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.

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References (25)

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Quantum time uncertainty in Schwarzschild–anti-de Sitter black holes

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