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Hauptverfasser: Garcia-Saenz, Sebastian, Guo, Guangzhou, Wang, Peng, Wang, Xinmiao
Format: Preprint
Veröffentlicht: 2025
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Online-Zugang:https://arxiv.org/abs/2501.01055
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author Garcia-Saenz, Sebastian
Guo, Guangzhou
Wang, Peng
Wang, Xinmiao
author_facet Garcia-Saenz, Sebastian
Guo, Guangzhou
Wang, Peng
Wang, Xinmiao
contents We report on the potential occurrence of a numerical instability in the long-time simulation of black holes using the Baumgarte-Shapiro-Shibata-Nakamura formulation of numerical relativity, even in the simple set-up of a Schwarzschild black hole. Through extensive numerical experiments, we identify that this "late-time instability" arises from accumulated violations of the momentum constraint. To address this issue, we propose two modified versions of the so-called conformal covariant Z4 scheme, designed to propagate momentum constraint violations without damping. Our results demonstrate that these alternative formulations, which we refer to as CCZ4' and CCZ3, effectively resolve the late-time numerical instability not only in Schwarzschild spacetimes but also in black hole spacetimes with matter fields. Notably, by preventing damping of the momentum constraint violation, the Hamiltonian constraint damping can be significantly increased, which plays a crucial role in stabilizing long-term evolution in our proposed schemes.
format Preprint
id arxiv_https___arxiv_org_abs_2501_01055
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Stable long-term evolution in numerical relativity
Garcia-Saenz, Sebastian
Guo, Guangzhou
Wang, Peng
Wang, Xinmiao
General Relativity and Quantum Cosmology
High Energy Physics - Theory
We report on the potential occurrence of a numerical instability in the long-time simulation of black holes using the Baumgarte-Shapiro-Shibata-Nakamura formulation of numerical relativity, even in the simple set-up of a Schwarzschild black hole. Through extensive numerical experiments, we identify that this "late-time instability" arises from accumulated violations of the momentum constraint. To address this issue, we propose two modified versions of the so-called conformal covariant Z4 scheme, designed to propagate momentum constraint violations without damping. Our results demonstrate that these alternative formulations, which we refer to as CCZ4' and CCZ3, effectively resolve the late-time numerical instability not only in Schwarzschild spacetimes but also in black hole spacetimes with matter fields. Notably, by preventing damping of the momentum constraint violation, the Hamiltonian constraint damping can be significantly increased, which plays a crucial role in stabilizing long-term evolution in our proposed schemes.
title Stable long-term evolution in numerical relativity
topic General Relativity and Quantum Cosmology
High Energy Physics - Theory
url https://arxiv.org/abs/2501.01055