Scalar averaging in Szekeres dust models Available to Purchase

We consider a formalism of weighed proper volume scalar averages (the "q-average") for the study of quasi-spherical Szekeres models. We show that the q-average of the main fluid flow covariant scalars are spherically symmetric and satisfy FLRW evolution laws, so that fluctuations and perturbations with respect to these averages provide a full description of the deviation of the models from homogeneity and spherical symmetry. The main proper tensors of the models are given in terms of these fluctuations, with the averages of scalar invariant contractions expressed as second order statistical moments of the density and Hubble scalar expansion. We discuss a possible application of this formalism in connection to a gravitational entropy functional in which entropy production is directly related to a negative statistical correlation between density and velocity fluctuations.