One of the major obstacles to testing alternative theories of gravity with gravitational-wave data from merging binaries of compact objects is the formulation of their field equations, which is often mathematically ill-suited for time evolutions. A possible way to address these delicate shortcomings is the fixing-the-equations approach, which was developed to control the behavior of the high-frequency modes of the solutions and the potentially significant flow toward ultraviolet modes. This is particularly worrisome in gravitational collapse, where even black hole formation might be insufficient to shield regions of the spacetime where these pathologies might arise. Here, we focus (as a representative example) on scalar-Gauss-Bonnet gravity, a theory that can lead to ill-posed dynamical evolutions, but with intriguing stationary black hole physics. We study the spherical collapse of a scalar pulse to a black hole in the fixing-the-equations approach, comparing the early stages of the evolution with the unfixed theory and the later stages with its stationary limit. With this approach, we are able to evolve past problematic regions in the original theory, resolve black hole collapse, and connect with the static black hole solutions. Our method can thus be regarded as providing a weak completion of the original theory, and the observed behavior lends support for considering previously found black hole solutions as a natural outcome of collapse scenarios.

中文翻译：

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修复标量-高斯-发动机罩重力的动态演化

用来自合并致密天体的双星的引力波数据来测试替代引力理论的主要障碍之一是它们的场方程的公式化，这在数学上通常不适合时间演化。解决这些微妙缺点的一种可能方法是固定方程方法，该方法旨在控制溶液的高频模式的行为以及朝向紫外模式的潜在显着流动。这在引力坍缩中尤其令人担忧，在这种情况下，即使是黑洞的形成也可能不足以屏蔽可能出现这些病症的时空区域。在这里，我们（作为一个代表性的例子）关注标量-高斯-博内引力，这是一种可以导致不适定动力学演化的理论，但具有有趣的静止黑洞物理学。我们研究了固定方程中标量脉冲对黑洞的球面坍缩方法，将演化的早期阶段与不固定理论进行比较，将后期阶段与其静止极限进行比较。通过这种方法，我们能够超越原始理论中的问题区域，解决黑洞坍缩问题，并与静态黑洞解决方案联系起来。因此，我们的方法可以被认为是对原始理论的弱补充，并且观察到的行为为将先前发现的黑洞解决方案视为坍缩情景的自然结果提供了支持。