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

TL;DR

This paper investigates whether a minimum time uncertainty exists in Schwarzschild-anti-de Sitter black holes, finding that perturbative approaches suggest a nonzero uncertainty, while nonperturbative methods allow arbitrarily precise time measurements.

Contribution

It compares perturbative and nonperturbative quantum gravity approaches to time uncertainty in black holes with a cosmological constant.

Findings

Perturbative approach indicates a nonzero minimum time uncertainty.

Nonperturbative approach allows arbitrarily high time resolution.

The cosmological constant influences the presence of time uncertainty.

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.