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Averaging and exact perturbations in LTB dust models | | Roberto A. Sussman
; | | Date: |
10 Sep 2012 | | Abstract: | We introduce a scalar weighed average ("q-average") acting on concentric
comoving domains in spherically symmetric Lemaitre-Tolman-Bondi (LTB) dust
models. The resulting averaging formalism allows for an elegant coordinate
independent dynamical study of the models, providing as well a valuable
theoretical insight on the properties of scalar averaging in inhomogeneous
spacetimes. The q-averages of those covariant scalars common to FLRW models
(the "q-scalars") identically satisfy FLRW evolution laws and determine for
every domain a unique FLRW background state. All curvature and kinematic proper
tensors and their invariant contractions are expressible in terms of the
q-scalars and their linear and quadratic local fluctuations, which convey the
effects of inhomogeneity through the ratio of Weyl to Ricci curvature
invariants and the magnitude of radial gradients. We define also non-local
fluctuations associated with the intuitive notion of a "contrast" with respect
to FLRW reference averaged values assigned to a whole domain or time slice. The
q-averages of local and non-local quadratic fluctuations are directly and
exactly related to statistical correlation moments of the density and Hubble
expansion scalar. The evolution equations for the q-scalars and suitably
defined perturbations completely determine the dynamics of the models without
the back-reaction correlation terms of Buchert’s average. A rigorous formalism
of exact spherical non-linear perturbations can be defined over a formal FLRW
background state associated to the q-scalars, recovering the standard results
of linear perturbation theory in the appropriate limit. We briefly explore the
possible application of this formalism to open theoretical issues, such as the
relation between the growth of inhomogeneity and a definition of gravitational
entropy. | | Source: | arXiv, 1209.1962 | | Services: | Forum | Review | PDF | Favorites | |
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