AI 中文总结
研究在Spectre代码中实现方程固定方法，引入共动驱动方程推广，模拟sGB引力中低偏心双黑洞，得到近40个GW周期的高精度含记忆波形。
AI 中文摘要
我们在Spectre（一种采用伪谱间断Galerkin格式的数值相对论（NR）代码）中实现了“方程固定”方法[Phys.Rev.D 96 (2017) 8, 084043]，以在著名的移位对称标量高斯-博内（sGB）引力中生成长且精确的NR波形。为实现这一目标，我们引入了一类新的共动驱动方程，该方程利用了准圆双星系统的近似对称性，旨在恢复全耦合理论的精确（准）稳态解。我们将单个黑洞（BH）解与解析预测进行了验证，结果表明，即使对于处于早期旋近阶段的双黑洞，其固有BH量对驱动方程中的时间尺度也相对不敏感。我们关注了张量的驱动方程方案，给出了一个示例，说明将张量分量视为标量处理会如何在长时间尺度上导致不期望的行为，包括BH自旋的虚假增长。我们为共动驱动提供了更合适的张量情况推广，该推广可避免这些问题。总体而言，我们的实现利用了 eccentricity 缩减和波提取的最先进方法（结合柯西特征演化）来模拟 eccentricity ≲10⁻³的系统。我们获得了在近40个引力波（GW）周期内相位误差≲O(1) rad的波形，该波形自然包含了记忆效应贡献。
英文摘要
We implement the "fixing-the-equations" approach [Phys.Rev.D 96 (2017) 8, 084043] in spectre, an NR code using a pseudo-spectral discontinuous Galerkin scheme, to produce long and accurate NR waveforms in the well-known shift-symmetric version of scalar Gauss-Bonnet (sGB) gravity. To achieve this, we introduce a new family of comoving driver equations that exploits the approximate symmetries of quasicircular binary systems and is designed to recover the exact (quasi-)stationary solutions of the fully-coupled theory. We validate our single black hole (BH) solutions against analytic predictions and show that, even for binary BHs in the early inspiral, the intrinsic BH quantities are relatively insensitive to the timescales entering the driver equation. Attention is given to the prescription of driver equations for tensors, for which we give an example of how treating tensor components as scalars can lead to undesired behaviour over long timescales, including spurious growth of the BH spins. A more appropriate generalization to the tensor case is given for the comoving driver, which is shown to avoid these issues. Overall, our implementation leverages state-of-the-art methods for eccentricity reduction and wave extraction with Cauchy Characteristic Evolution to simulate systems with eccentricity $\lesssim 10^{-3}$. We obtain waveforms with phase errors $\lesssim \mathcal{O}(1) \, \mathrm{rad}$ over almost 40 GW-cycles, which naturally incorporate memory contributions.
Comments22+3 pages, 19 figures
