Correlations across horizons in quantum cosmology

Abstract

Different spacetime regions separated by horizons are not related to each other. We know that this statement holds for classical spacetimes. In this paper we carry out a canonical quantization of a Kantowski-Sachs minisuperspace model whose classical solutions exhibit both an event horizon and a cosmological horizon in order to check whether the above statement also holds from the quantum gravitational point of view. Our analysis shows that in fact this is not the case: Quantum gravitational states with support in spacetime configurations that exclusively describe either the region between horizons or outside them are not consistent in the sense that there exist unitary operators describing a natural notion of evolution that connect them. In other words, unitarity is only preserved in this quantization when dealing with the whole spacetime and not in each region separately.