Effects of quantum geometry on the decoherence induced by black holes

Abstract

Recently, it has been shown that a quantum system held in spatial superposition and then eventually recombined does experience decoherence from black hole horizons, at a level increasing linearly with the time the superposition has been kept open. In this, the effects of the horizon have been derived using a classical spacetime picture for the latter. In the present note we point out that quantum aspects of the geometry itself of the quantum black hole could significantly affect the results. In a specific effective implementation of the quantum geometry in terms of a minimal length and ensuing minimal area, it appears in particular that, for selected values of the quantum of area proposed on various grounds in the literature, the decoherence induced by the horizon turns out to be limited to negligibly small values.

Figures (1)

• Figure 1: Qualitative sketch of the behavior of the decoherence functional $\mathds{D}$ for different sizes of cutoffs $\Omega_0$ or no cutoff at all ($\Omega_0=0$). The saturation values obtained in Regime III for the cutoffs proposed in the literature that are of the order of $\Omega_0\sim a$ are many orders of magnitude lower than unity, see equation \ref{['eq:dsatval']}, thus rendering the decoherence negligibly small. The behavior at the transitions between the different regimes is not accurately resolved in this sketch as the main purpose is a visualization of the three different regimes.