IX Black Hole Workshop

Guimarães 19-20 December 2016

The necessary information to distinguish a local inhomogeneous mass density field from its spatial average on a compact domain of the universe can be measured by relative information entropy. The Kullback-Leibler (KL) formula arises very naturally in this context, however, it provides a very complicated way to compute the mutual information between spatially separated but causally connected regions of the universe in a realistic, inhomogeneous model. To circumvent this issue, by considering a parametric extension of the KL measure, I present a model to describe the mutual information which is entangled via the gravitational field equations. I show that the Tsallis relative entropy can be a good approximation in the case of small inhomogeneities, and for measuring the independent relative information inside the domain, the Rényi relative entropy can be a formula.