2015
DOI: 10.1088/1475-7516/2015/03/053
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Evolution of linear perturbations in Lemaítre-Tolman-Bondi void models

Abstract: We study the evolution of linear perturbations in a Lemaître-Tolman-Bondi (LTB) void model with realistic cosmological initial conditions. Linear perturbation theory in LTB models is substantially more complicated than in standard Friedmann universes as the inhomogeneous background causes gauge-invariant perturbations couple at first order. As shown by Clarkson et al. (2009) ([21]), the evolution is constrained by a system of linear partial differential equations which need to be integrated numerically. We pre… Show more

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Cited by 7 publications
(20 citation statements)
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References 73 publications
(201 reference statements)
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“…The linearised Einstein's equations (34) and (35) show that the wave equation for '+' polarization is inhomogeneous, while that for '×' polarization is homogeneous [35] when the GW propagates along the z-direction. The dispersion relations (38) and (39) show that the two polarizations have slightly different wave-vectors, the difference being contributed by the energy-momentum tensor.…”
Section: Discussionmentioning
confidence: 99%
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“…The linearised Einstein's equations (34) and (35) show that the wave equation for '+' polarization is inhomogeneous, while that for '×' polarization is homogeneous [35] when the GW propagates along the z-direction. The dispersion relations (38) and (39) show that the two polarizations have slightly different wave-vectors, the difference being contributed by the energy-momentum tensor.…”
Section: Discussionmentioning
confidence: 99%
“…so that a plane gravitational wave of frequency ω is characterised by wave-vectors k 11 and k 12 in its '+' and '×'polarization modes respectively. Substituting (36) in equation (34), and (37) in equation (35), and solving for the wave-vectors, the following dispersion relations are obtained:…”
Section: B Linearised Einstein's Equations and Their Solutionsmentioning
confidence: 99%
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“…(4.1), no propagating mode generated in the domain of interest and being reflected at r * should re-enter it within the integration time interval [t min , t max ]. For further details and figures on the construction of boundary conditions for this setup, the reader is referred to ( [32]) and ( [33]).…”
Section: Initial and Boundary Conditionsmentioning
confidence: 99%
“…where δ µ γ is the Kronecker delta. The metric tensor allows us to define a unit time-like vector field orthogonal to constant-time hypersurfaces, 15) subject to the constraint n µ n µ = −1 .…”
Section: General Background Equationsmentioning
confidence: 99%