Constraint and gauge shocks in one-dimensional numerical relativity

Bernd Reimann, Miguel Alcubierre, José A. González, and Darío Núñez
Phys. Rev. D 71, 064021 – Published 23 March 2005

Abstract

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-Massó–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.

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  • Received 18 November 2004

DOI:https://doi.org/10.1103/PhysRevD.71.064021

©2005 American Physical Society

Authors & Affiliations

Bernd Reimann1,2, Miguel Alcubierre1, José A. González3, and Darío Núñez1

  • 1Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, A.P. 70-543, México D.F. 04510, México
  • 2Max Planck Institut für Gravitationsphysik, Albert Einstein Institut, Am Mühlenberg 1, 14476 Golm, Germany
  • 3Institute for Gravitational Physics and Geometry, Penn State University, University Park, Pennsylvania 16802, USA

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Issue

Vol. 71, Iss. 6 — 15 March 2005

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