2004/11/30 by Bernd Reimann, Miguel Alcubierre, José A. González +1 · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Pulsars and Gravitational Waves Research #gr-qc
paper · pdf · doi:10.1103/physrevd.71.064021
published as Phys.Rev. D71 (2005) 064021 · 19 pages, 8 figures and 1 table, revised version including several amendments suggested by the referee
arxiv created 2005/03/03 · openalex publication_date 2005/03/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study how different types of blowups can occur in systems of hyperbolic evolution equations of the type found in general relativity. In particular, we discuss two independent criteria that can be used to determine when such blowups can be expected. One criteria is related to the so-called geometric blowup leading to gradient catastrophes, while the other is based upon the ODE-mechanism leading to blowups within finite time. We show how both mechanisms work in the case of a simple one-dimensional wave equation with a dynamic wave speed and sources, and later explore how those blowups can appear in one-dimensional numerical relativity. In the latter case we recover the well known ``gauge shocks'' associated with Bona-Mass'o--type slicing conditions. However, a crucial result of this study has been the identification of a second family of blowups associated with the way in which the constraints have been used to construct a hyperbolic formulation. We call these blowups ``constraint shocks'' and show that they are formulation specific, and that choices can be made to eliminate them or at least make them less severe.