Unconstrained hyperboloidal evolution of black holes in spherical symmetry with GBSSN and Z4c

Abstract

We consider unconstrained evolution schemes for the hyperboloidal initial value problem in numerical relativity as a promising candidate for the optimally efficient numerical treatment of radiating compact objects. Here, spherical symmetry already poses nontrivial problems and constitutes an important first step to regularize the resulting singular PDEs. We evolve the Einstein equations in their generalized BSSN and Z4 formulations coupled to a massless self-gravitating scalar field. Stable numerical evolutions are achieved for black hole initial data, and critically rely on the construction of appropriate gauge conditions.

6 pages, 5 figures

References in corpus (6)

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• Hyperboloidal evolution with the Einstein equations
• Gravitational perturbations of Schwarzschild spacetime at null infinity and the hyperboloidal initial value problem
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Cited by in corpus (6)

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• Merging black holes with Cauchy-characteristic matching: Computation of late-time tails
• Spherically symmetric black hole spacetimes on hyperboloidal slices
• Height-function-based 4D reference metrics for hyperboloidal evolution
• Peeling in Generalized Harmonic Gauge
• Nonlinear Evolution of unstable Charged de Sitter Black Holes with Hyperboloidal Formalism