Initial data for perturbed Kerr black holes on hyperboloidal slices

Abstract

We construct initial data corresponding to a single perturbed Kerr black hole in vacuum. These data are defined on specific hyperboloidal ("ACMC-") slices on which the mean extrinsic curvature K asymptotically approaches a constant at future null infinity scri+. More precisely, we require that K obeys the Taylor expansion K=K0 + s^4 where K0 is a constant and s describes a compactified spatial coordinate such that scri+ is represented by s=0. We excise the singular interior of the black hole and assume a marginally outer trapped surface as inner boundary of the computational domain. The momentum and Hamiltonian constraints are solved by means of pseudo-spectral methods and we find exponential rates of convergence of our numerical solutions. Some physical properties of the initial data are studied with the calculation of the Bondi Mass, together with a multipole decomposition of the horizon. We probe the standard picture of gravitational collapse by assessing a family of Penrose-like inequalities and discuss in particular their rigidity aspects. Dynamical evolutions are planned in a future project.

35 pages, 11 figures, Version published in CQG

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Cited by in corpus (15)

• Spectral decomposition of black-hole perturbations on hyperboloidal slices
• Perturbing the perturbed: Stability of quasinormal modes in presence of a positive cosmological constant
• Hyperboloidal slicing approach to quasi-normal mode expansions: the Reissner-Nordström case
• Hyperboloidal framework for the Kerr spacetime
• Hyperboloidal approach for static spherically symmetric spacetimes: a didactical introduction and applications in black-hole physics
• Axisymmetric fully spectral code for hyperbolic equations
• Hyperboloidal Approach to Quasinormal Modes
• Spherically symmetric black hole spacetimes on hyperboloidal slices
• Free evolution of the hyperboloidal initial value problem in spherical symmetry
• Three dimensional distorted black holes: using the Galerkin-Collocation method
• Discontinuous Galerkin scheme for elliptic equations on extremely stretched grids
• Hyperboloidal initial data without logarithmic singularities
• Slicing black hole spacetimes
• Hyperboloidal neutron star and black hole initial data in spherical symmetry
• Hyperboloidal method for frequency-domain self-force calculations