Evolution of linear perturbations in spherically symmetric dust spacetimes

Abstract

We present results from a numerical code implementing a new method to solve the master equations describing the evolution of linear perturbations in a spherically symmetric but inhomogeneous background. This method can be used to simulate several configurations of physical interest, such as relativistic corrections to structure formation, the lensing of gravitational waves and the evolution of perturbations in a cosmological void model. This paper focuses on the latter problem, i.e. structure formation in a Hubble scale void in the linear regime. This is considerably more complicated than linear perturbations of a homogeneous and isotropic background because the inhomogeneous background leads to coupling between density perturbations and rotational modes of the spacetime geometry, as well as gravitational waves. Previous analyses of this problem ignored this coupling in the hope that the approximation does not affect the overall dynamics of structure formation in such models. We show that for a giga-parsec void, the evolution of the density contrast is well approximated by the previously studied decoupled evolution only for very large-scale modes. However, the evolution of the gravitational potentials within the void is inaccurate at more than the $10\%$ level, and is even worse on small scales.

24 pages, 11 figures, typos corrected, reference and figure added, version accepted by CQG

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Cited by in corpus (10)

• Probing spatial homogeneity with LTB models: a detailed discussion
• Propagation of Axial and Polar Gravitational Waves in Kantowski-Sachs Universe
• Evolution of linear perturbations in Lemaître-Tolman-Bondi void models
• Axial Gravitational Waves in Bianchi I Universe
• Comparison of two approximation schemes for solving perturbations in a LTB cosmological model
• On the propagation of gravitational waves in matter-filled Bianchi I universe
• Newtonian self-gravitating system in a relativistic huge void universe model
• Linear perturbations in spherically symmetric dust cosmologies including a cosmological constant
• The gravitational wave background induced by nonlinear interactions between isotropic inhomogeneities and anisotropic inhomogeneous density perturbations
• Light propagation in linearly perturbed $\Lambda$LTB models