Quantum Decoherence in a Four-Dimensional Black Hole Background

TL;DR

This paper investigates quantum decoherence effects caused by logarithmic divergences in the scalar field density matrix around a four-dimensional Einstein-Yang-Mills black hole, revealing new insights into black hole entropy and quantum field behavior.

Contribution

It demonstrates a link between entropy divergences and quantum decoherence in black hole backgrounds, introducing a non-commutator term in the quantum Liouville equation.

Findings

Logarithmic divergence in the scalar field density matrix.

Divergence related to black hole entropy, not renormalizable.

Induces a non-commutator term leading to decoherence.

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. As the latter decays, the logarithmic divergence induces a non-commutator term $\nd{\delta H}\rho$ in the quantum Liouville equation for the density matrix $\rho$ of the scalar field, leading to quantum decoherence. The order of magnitude of $\nd{\delta H}$ is $\mu^2/M_P$, where $\mu$ is the mass of the scalar particle.