Quantum Decoherence in a Four-Dimensional Black Hole Background

Abstract

We display a logarithmic divergence in the density matrix of a scalar field in the presence of an Einstein–Yang–Mills black hole in four dimensions. This divergence is related to a previously-found logarithmic divergence in the entropy of the scalar field, which cannot be absorbed into a renormalization of the Hawking–Bekenstein entropy of the black hole. Motivated by the fact that the cutoff in this divergence varies as the latter decays, by an analysis of black holes in two-dimensional string models and by studies of D-brane dynamics in higher dimensions, we propose that the renormalization scale variable be identified with time. In this case, the logarithmic divergence we find induces a non-commutator term [Formula: see text] in the quantum Liouville equation for the time evolution of the density matrix ρ of the scalar field, leading to quantum decoherence. The order of magnitude of [Formula: see text] is μ2/M P , where μ is the mass of the scalar particle.