有效场论的边缘：二次引力中的近极值黑洞
Living on the Edge of Effective Field Theory: Near-Extremal Black Holes in Quadratic Gravity
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中文总结 AI 辅助
该研究在含动力学标量的二次引力中，用伪谱方法构造近极值黑洞解，对比了动力学Chern-Simons与标量Gauss-Bonnet引力中近极值解的极限行为，诊断了有效场论展开的失效并给出微扰有效性估计。
中文摘要 AI 辅助
近极值黑洞可放大广义相对论的高阶导数修正，使其成为探测引力有效场论微扰控制的锐利工具。我们在含动力学标量自由度的二次引力（聚焦于动力学Chern-Simons引力与标量Gauss-Bonnet引力）中研究该问题。采用伪谱方法，我们构造了固定表面重力与固定视界角速度下的快速旋转外部解，并追踪该受控族向极值态的演化。在动力学Chern-Simons引力中，该序列趋近于渐近平坦的极值外部解，其近视界极限与动力学Chern-Simons变形的近视界极值Kerr几何一致，并继承了其增强的SO(2,1)×U(1)对称性。在标量Gauss-Bonnet引力中，相同的极限过程表现不同：标量在视界处产生不可避免的对数奇点，外部度规在视界附近形成小边界层，且标量Gauss-Bonnet变形的近视界极值解与正则渐近平坦外部解不连通。随后我们利用曲率不变量与潮汐力诊断微扰有效场论展开的失效，发现即使自由下落观测者测得的潮汐力随表面重力的负幂次发散，标量曲率不变量仍可在视界处保持有限。这些结果区分了近极值处有效场论失效的不同概念，并提供了可与当前动力学Chern-Simons及标量Gauss-Bonnet耦合常数界对比的微扰有效性估计。
英文摘要
Near-extremal black holes can amplify higher-derivative corrections to general relativity, making them sharp probes of the perturbative control of gravitational effective field theory. We study this question in quadratic gravity with a dynamical scalar degree of freedom, focusing on dynamical Chern-Simons and scalar Gauss-Bonnet gravity. Using pseudospectral methods, we construct rapidly rotating exterior solutions at fixed surface gravity and fixed horizon angular velocity, and follow this controlled family toward extremality. In dynamical Chern-Simons gravity, the sequence approaches an asymptotically flat extremal exterior whose near-horizon limit agrees with the dynamical-Chern-Simons-deformed near-horizon extremal Kerr geometry and inherits its enhanced $SO(2,1)\times U(1)$ symmetry. In scalar Gauss-Bonnet gravity, the same limiting procedure behaves differently: the scalar develops an unavoidable logarithmic singularity at the horizon, the exterior metric develops a small boundary layer near the horizon, and the scalar-Gauss-Bonnet-deformed near-horizon extremal solution is not connected to a regular asymptotically flat exterior. We then use curvature invariants and tidal forces to diagnose the breakdown of the perturbative effective-field-theory expansion. We find that scalar curvature invariants can remain finite at the horizon even when tidal forces measured by infalling observers diverge as inverse powers of the surface gravity. These results separate distinct notions of effective-field-theory breakdown near extremality and provide a perturbative validity estimate that can be compared with current bounds on the dynamical Chern-Simons and scalar-Gauss-Bonnet couplings.
