Stability analysis and improvement of the covariant BSSN formulation against the FLRW spacetime background
<|reference_start|>Stability analysis and improvement of the covariant BSSN formulation against the FLRW spacetime background: In this study, we investigate the numerical stability of the covariant Baumgarte--Shapiro--Shibata--Nakamura (cBSSN) formulation against the Friedmann--Lema\^itre--Robertson--Walker spacetime. To evaluate the numerical stability, we calculate the constraint amplification factor by the eigenvalue analysis of the evolution of the constraint. We propose a modification to the time evolution equations of the cBSSN formulation for a higher numerical stability. Furthermore, we perform numerical simulations using the modified formulation to confirm its improved stability.<|reference_end|>
@article{hoshino2024stability,
    title={Stability analysis and improvement of the covariant BSSN formulation
  against the FLRW spacetime background},
    author={Hidetomo Hoshino, Takuya Tsuchiya, Gen Yoneda},
    journal={arXiv preprint arXiv:2407.14305},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.14305},
    primaryClass={gr-qc cs.NA math.NA}
}