Quasi-local variables, non-linear perturbations and back-reaction in spherically symmetric spacetimes

Abstract

We introduce a quasi-local integral functional and scalar quasi-local variables to examine a wide class of spherically symmetric inhomogeneous spacetimes that generalize the Lemaitre-Tolman-Bondi (LTB) dust solutions ("LTB" spacetimes). By using these variables, we can transform the fluid flow evolution equations into evolution equations for non-linear, covariant, gauge--invariant perturbations of Friedman-Lemaitre-Robertson-Walker (FLRW) cosmologies. In the linear limit, we obtain spherical perturbations in the synchronous gauge under the long wavelength approximation. The formalism has a significant potential for cosmological applications, as it allows one to examine a wide variety of sources with different "equations of state", generalizing known FLRW solutions to idealized but non-trivial and non-linear inhomogeneous conditions. The quasi-local functional can be reformulated as a weighed proper volume average distribution, with the weight factor given by a scalar invariant related to the quasi-local mass-energy function. The back-reaction terms, emerging in Buchert's proper averaging formalism, can be expressed as differences between fluctuations of averaged and quasi-local energy densities. By comparing this average with the weighed quasi-local one, we can define a binding energy functional related to spatial gradients of the averaged and quasi-local variables that appear in the back-reaction terms.

24 pages IOP LaTeX style, has no figures

References in corpus (10)

• Dark Matter and Dark Energy
• Cosmological Solutions in Macroscopic Gravity
• Testing backreaction effects with observations
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• On the onset of cosmological backreaction
• Can inhomogeneties accelerate the cosmic volume expansion?
• Apparent and average acceleration of the Universe
• Averaging and Cosmological Observations
• Space-time Averages of Classical Physical Fields
• On a Quasi-Local Energy Outside the Cosmological Horizon

Cited by in corpus (9)

• What is dust? - Physical foundations of the averaging problem in cosmology
• Quasi-local variables in spherical symmetry: numerical applications to dark matter and dark energy sources
• Chaplygin gas and effective description of inhomogeneous universe models in general relativity
• On spatial volume averaging in Lema\^ıtre--Tolman--Bondi dust models. Part I: back reaction, spacial curvature and binding energy
• Quasi-local variables and inhomogeneous cosmological sources with spherical symmetry
• On the role of shear in cosmological averaging II: large voids, non-empty voids and a network of different voids
• Velocity and velocity bounds in static spherically symmetric metrics
• Gravitational energy as dark energy: Cosmic structure and apparent acceleration
• Shear viscosity, relaxation and collision times in spherically symmetric spacetimes