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Stability analysis and improvement of the covariant BSSN formulation against the FLRW spacetime background

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Hidetomo Hoshino, Takuya Tsuchiya, Gen Yoneda

General Relativity and Quantum Cosmology · Submitted 19 Jul 2024

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Furthermore, we perform numerical simulations using the modified formulation to confirm its improved stability.

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arXiv ID2407.14305 (version 1)
Pith IDK3AZ5JRJ, Pith's permanent record of this paper and its review
CitationGen Yoneda, Hidetomo Hoshino, Takuya Tsuchiya. "Stability analysis and improvement of the covariant BSSN formulation against the FLRW spacetime background." arXiv:2407.14305 (2024). https://pith.science/paper/K3AZ5JRJ
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,600 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.05 · human participants 0.01 · controlled comparison 0.34 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.30 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

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.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 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. contribution 0.93 0.80 0.05 unclear 0.56
s1 To evaluate the numerical stability, we calculate the constraint amplification factor by the eigenvalue analysis of the evolution of the constraint. method 1.00 0.94 0.03 asserted 0.99
s2 We propose a modification to the time evolution equations of the cBSSN formulation for a higher numerical stability. contribution 0.98 0.93 0.28 asserted 0.97
s3 Furthermore, we perform numerical simulations using the modified formulation to confirm its improved stability. method 0.41 0.97 0.43 asserted 0.98

What kind of paper the classifier reports this is: method or tool 0.76 · evidence from simulation or computation 0.98.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

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.

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