Publication: Quantum time uncertainty in Schwarzschild-anti-de Sitter black holes
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2007-08
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Amer Physical Soc
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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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© 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.
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