Hyperboloidal slices for the wave equation of Kerr-Schild metrics and numerical applications

Abstract

We present new results from two open source codes, using finite differencing and pseudo-spectral methods for the wave equations in (3+1) dimensions. We use a hyperboloidal transformation which allows direct access to null infinity and simplifies the control over characteristic speeds on Kerr-Schild backgrounds. We show that this method is ideal for attaching hyperboloidal slices or for adapting the numerical resolution in certain spacetime regions. As an example application, we study late-time Kerr tails of sub-dominant modes and obtain new insight into the splitting of decay rates. The involved conformal wave equation is freed of formally singular terms whose numerical evaluation might be problematically close to future null infinity.

15 pages, 12 figures

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Cited by in corpus (11)

• 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
• Caustic echoes from a Schwarzschild black hole
• Intermediate behavior of Kerr tails
• Mode coupling mechanism for late-time Kerr tails
• Hyperboloidal Approach to Quasinormal Modes
• R-mode frequencies of rapidly and differentially rotating relativistic neutron stars
• Scalar Fields in Black Hole Spacetimes
• Numerical investigation of the late-time tails of the solutions of the Fackerell-Ipser equation
• Hyperboloidal Method for Quasinormal Modes of Non-Relativistic Operators