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arXiv · 1409.3476

Fully relativistic nonlinear cosmological evolution in spherical symmetry using the BSSN formalism

Jeremy Rekier·Isabel Cordero-Carrion·Andre Fuzfa
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Abstract

We present a fully relativistic numerical method for the study of cosmological problems using the Baumgarte-Shapiro-Shibata-Nakamura formalism on a dynamical Friedmann-Lema\^itre-Robertson-Walker background. This has many potential applications including the study of the growth of structures beyond the linear regime. We present one such application by reproducing the Lema\^itre-Tolman-Bondi solution for the collapse of pressureless matter with arbitrary lapse function. The regular and smooth numerical solution at the center of coordinates proceeds in a natural way by relying on the Partially Implicit Runge-Kutta algorithm described in Montero and Cordero-Carri\'on [arXiv:1211.5930]. We generalize the usual radiative outer boundary condition to the case of a dynamical background and show the stability and convergence properties of the method in the study of pure gauge dynamics on a de Sitter background.

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Jeremy Rekier, Isabel Cordero-Carrion, Andre Fuzfa. 2014-09-11. Fully relativistic nonlinear cosmological evolution in spherical symmetry using the BSSN formalism. https://doi.org/10.1103/physrevd.91.024025

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