Type II critical collapse on a single fixed grid: a gauge-driven ingoing boundary method
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Type II critical collapse on a single fixed grid: a gauge-driven ingoing boundary method Oliver Rinne1,2 Received: 28 August 2020 / Accepted: 16 November 2020 © The Author(s) 2020
Abstract We develop a numerical method suitable for gravitational collapse based on Cauchy evolution with an ingoing characteristic boundary. Unlike similar methods proposed recently (Ripley; Bieri et al. in Class Quantum Grav 37:045015, 2020), the numerical grid remains fixed during the evolution and no points need to be removed or added. Increasing coordinate refinement of the central region as the field collapses is achieved solely through the choice of spatial gauge and particularly its boundary condition. We apply this method to study critical collapse of a massless scalar field in spherical symmetry using maximal slicing and isotropic coordinates. Known results on mass scaling, discrete self-similarity and universality of the critical solution (Choptuik in Phys Rev Lett 70:9, 1993) are reproduced using this considerably simpler numerical method. Keywords Numerical relativity · Boundary conditions · Black holes · Critical collapse
Contents 1 Introduction . . . . . . . . . . . . 2 Formulation of the model . . . . . 2.1 Choice of gauge and variables 2.2 Field equations . . . . . . . . 2.3 Boundary conditions . . . . . 3 Numerical methods . . . . . . . . 3.1 Evolution scheme . . . . . . . 3.2 Discretisation . . . . . . . . . 3.3 ODE solvers . . . . . . . . . .
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Oliver Rinne [email protected]
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Hochschule für Technik und Wirtschaft Berlin, Treskowallee 8, 10318 Berlin, Germany
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Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, 14476 Potsdam, Germany 0123456789().: V,-vol
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3.4 Termination criteria . . . . . . . . . . . . . . . . . . . . . . . 4 Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Initial data and bisection . . . . . . . . . . . . . . . . . . . . 4.2 Choosing the outer boundary radius . . . . . . . . . . . . . . 4.3 Mass scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Discrete self-similarity and universality of the critical solution 5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
O. Rinne . . . . . . . .
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