标题： 高曲率引力的因果结构 显示英文标题

标题： Causal Structure of Higher Curvature Gravity

摘要： 在本文中，我们分析了广义二次引力（GQG）和爱因斯坦三次引力（ECG）的因果结构。众所周知，在高曲率理论中，引力子可能表现出超光速传播，这使得基于零曲线的传统因果结构定义不再适用。相反，必须使用最快传播模式来定义因果结构，这些模式沿特征曲面传播。高曲率理论中的超光速传播对黑洞有重要影响。具体来说，如果黑洞的Killing视界不是对应于最快传播模式的特征曲面，那么视界将无法作为因果屏障。我们的分析表明，具有真实四阶运动方程的GQG仅具有零特征，这意味着视界是特征曲面。此外，我们对ECG进行了详细的特征分析。我们证明在ECG中，所有零曲面都是特征曲面，但反之则不成立——存在非零特征曲面。特别是，在时空的代数分类中，我们在一个N型时空里识别出一个非零特征曲面。尽管ECG中存在多个特征曲面，但我们确定黑洞视界仍然是一个特征曲面。 显示英文摘要

摘要： In this paper, we analyze the causal structure of Generalized Quadratic Gravity (GQG) and Einsteinian Cubic Gravity (ECG). It is well known that gravitons in higher-curvature theories can exhibit superluminal propagation, rendering the conventional definition of causal structures based on null curves inadequate. Instead, the causal structure must be defined using the fastest propagating modes, which travel along characteristic surfaces. The superluminal propagation in higher-curvature theories has significant implications for black holes. Specifically, if the Killing horizon of a black hole is not a characteristic surface corresponding to the fastest propagating mode, the horizon can no longer function as a causal barrier. Our analysis demonstrates that GQG with a genuine fourth-order equation of motion possesses only null characteristics, implying that the horizon is a characteristic surface. Furthermore, we perform a detailed characteristic analysis of ECG. We show that while all null surfaces are characteristic surfaces in ECG, the converse is not true - there exist non-null characteristic surfaces. In particular, we identify a non-null characteristic surface in a Type N spacetime in the algebraic classification of spacetimes. Despite the existence of multiple characteristic surfaces in ECG, we establish that the black hole horizon remains a characteristic surface.