### Abstract

We have recently constructed a numerical code that evolves a spherically symmetric spacetime using a hyperbolic formulation of Einstein’s equations. For the case of a Schwarzschild black hole, this code works well at early times, but quickly becomes inaccurate on a time scale of [Formula Presented] where [Formula Presented] is the mass of the hole. We present an analytic method that facilitates the detection of instabilities. Using this method, we identify a term in the evolution equations that leads to a rapidly growing mode in the solution. After eliminating this term from the evolution equations by means of algebraic constraints, we can achieve free evolution for times exceeding [Formula Presented] We discuss the implications for three-dimensional simulations.

Original language | English (US) |
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Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 58 |

Issue number | 4 |

DOIs | |

State | Published - Jan 1 1998 |

### ASJC Scopus subject areas

- Nuclear and High Energy Physics
- Physics and Astronomy (miscellaneous)

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## Cite this

*Physical Review D - Particles, Fields, Gravitation and Cosmology*,

*58*(4). https://doi.org/10.1103/PhysRevD.58.044020