https://doi.org/10.1140/epjc/s10052-015-3334-8
Regular Article - Theoretical Physics
Kullback–Leibler entropy and Penrose conjecture in the Lemaître–Tolman–Bondi model
Department of Physics, College of Sciences, Northeastern University, Shenyang, 110819, China
* e-mail: linan@mail.neu.edu.cn
Received:
17
November
2014
Accepted:
26
February
2015
Published online:
11
March
2015
Our universe hosts various large-scale structures from voids to galaxy clusters, so it would be interesting to find some simple and reasonable measure to describe the inhomogeneities in the universe. We explore two different methods for this purpose: the Kullback–Leibler entropy and the Weyl curvature tensor. These two quantities characterize the deviation of the actual distribution of matter from the unperturbed background. We calculate these two measures in the spherically symmetric Lemaître–Tolman–Bondi model in the dust universe. Both exact and perturbative calculations are presented, and we observe that these two measures are in proportion up to second order.
© SIF and Springer-Verlag Berlin Heidelberg, 2015
