The non-linear perturbation of a black hole by gravitational waves. II. Quasinormal modes and the compactification problem

Abstract

Recently, Friedrich's Generalized Conformal Field Equations (GCFE) have been implemented numerically and global quantities such as the Bondi energy and the Bondi-Sachs mass loss have been successfully calculated directly on null-infinity. Although being an attractive option for studying global quantities by way of local differential geometrical methods, how viable are the GCFE for study of quantities arising in the physical space-time? In particular, how long can the evolution track phenomena that need a constant proper physical timestep to be accurately resolved? We address this question by studying the curvature oscillations induced on the Schwarzschild space-time by a non-linear gravitational perturbation. For small enough amplitudes, these are the well approximated by the linear quasinormal modes, where each mode rings at a frequency determined solely by the Schwarzschild mass. We find that the GCFE can indeed resolve these oscillations, which quickly approach the linear regime, but only for a short time before the compactification becomes ``too fast'' to handle numerically.

19 pages, 8 figures, submitted to CQG

References in corpus (3)

• Gravitational perturbations of Schwarzschild spacetime at null infinity and the hyperboloidal initial value problem
• The numerical initial boundary value problem for the generalized conformal field equations
• A new look at the Bondi-Sachs energy-momentum

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• Quasi-Local Black Hole Horizons: Recent Advances
• Merging black holes with Cauchy-characteristic matching: Computation of late-time tails
• Free Hyperboloidal Evolution of the Einstein-Maxwell-Klein-Gordon System