We present the first numerically stable nonlinear evolution for the leading-order gravitational effective field theory (quadratic gravity) in the spherically-symmetric sector. The formulation relies on (i) the harmonic gauge to cast the evolution system into quasilinear form (ii) the Cartoon method to reduce to spherical symīmetry in keeping with the harmonic gauge, and (iii) order reduction to first order (in time) by means of introducing auxiliary variables. The well posedness of the respective initial-value problem is numerically confirmed by evolving randomly perturbed flat-space and black-hole initial data. Our study serves as a proof-of-principle for the possibility of stable numerical evolution in the presence of higher derivatives.

中文翻译：

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球对称二次重力的非线性动力学

我们提出了球对称扇区中领先阶引力有效场理论（二次引力）的第一个数值稳定非线性演化。该公式依赖于 (i) 谐波规范将演化系统转换为拟线性形式 (ii) 卡通方法减少到与谐波规范一致的球对称，以及 (iii) 阶数减少到一阶（在时间上）引入辅助变量的方法。各个初始值问题的适定性通过演化随机扰动的平坦空间和黑洞初始数据在数值上得到证实。我们的研究作为在存在更高导数的情况下稳定数值演化的可能性的原理证明。