三维爱因斯坦-高斯-邦纳引力中的黑洞与标量传播
Black Holes and Scalar Propagation in Three-Dimensional Einstein--Gauss--Bonnet Gravity
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- University of Waterloo（滑铁卢大学）
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中文总结 AI 辅助
本文在三维标量-张量爱因斯坦-高斯-邦纳引力中推导出解析黑洞族，证明其解的唯一性，并分析扰动传播特性，发现标量信号可穿越视界，且特定边界条件下演化受限于AdS边界。
中文摘要 AI 辅助
我们在具有正耦合的三维标量-张量爱因斯坦-高斯-邦纳引力中推导出一个解析黑洞族。一个单一的隐式方程确定了静态圆形度规和随时间线性变化的标量。我们证明，这些解穷尽了具有所述AdS边界条件和标量中时间项固定非零系数的正则非极端外部解。耦合的度规和标量扰动具有一个传播自由度。在一个分支上，其动能系数为正，其方程在整个外部区域为双曲型，并且对于紧支撑的扰动，其体空间能量为正。标量信号可以向外穿过度规视界，因此外部演化需要来自内部的信息。对于具有原始度规和标量边界值固定的线性扰动，具有零速度的非零紧致初始主位移只能演化到它们首次接触AdS边界为止。我们从原始度规和标量方程推导出这一限制。
英文摘要
We derive an analytic black-hole family in three-dimensional scalar--tensor Einstein--Gauss--Bonnet gravity with positive coupling. A single implicit equation determines the static circular metric and a scalar linear in time. We show that these solutions exhaust regular nonextremal exteriors with the stated AdS boundary conditions and a fixed nonzero coefficient of time in the scalar. The coupled metric and scalar perturbations have one propagating degree of freedom. On one branch, its kinetic coefficient is positive, its equation is hyperbolic throughout the exterior, and its bulk spatial energy is positive for perturbations of compact support. Scalar signals can cross the metric horizon outward, so exterior evolution needs information from the interior. For linear perturbations with the original metric and scalar boundary values fixed, nonzero compact initial master displacements with zero velocity can evolve only until their first contact with the AdS boundary. We derive this restriction from the original metric and scalar equations.
