毛状霍恩德斯基引力中的光学景观与高能碰撞
Optical Landscapes and High-Energy Collisions in Hairy Horndeski Gravity
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中文总结 AI 辅助
本文研究毛状霍恩德斯基黑洞的类光测地线结构与高能粒子碰撞，推导光子球参数，发现极端构型下存在稳定光子球，且该构型下BSW效应的质心能量会发散。
中文摘要 AI 辅助
我们研究一类静态球对称毛状霍恩德斯基黑洞的类光测地线结构、光子球动力学及高能粒子碰撞。该时空以r=2M处的不变度规根和标量毛参数Q为特征，由表面重力κ|_{2M}划分为四个不同几何区域。我们推导了光子球半径r_ph及其动态稳定性判据的精确解析表达式，表明非极端区域中外在圆形类光轨道始终动态不稳定。关键在于，我们证明稳定光子球仅出现在极端构型（Q=-2M）中，此时它恰好与退化视界（r=2M）重合。我们认为这种视界束缚的稳定光子轨道是光和超相对论粒子的无限红移束缚态。最后，我们分析了下落类时测试粒子的巴尼亚多斯-西尔克-韦斯特（BSW）效应，证明临界碰撞的质心能量E_cm在极端阈值Q=-2M处严格按E_cm ∝ (r - r_h)^{-1/2}发散。
英文摘要
We investigate the null geodesic structure, photon sphere dynamics, and high-energy particle collisions within a class of static, spherically symmetric hairy Horndeski black holes. Characterized by an invariant metric root at $r = 2M$ and a scalar hair parameter $Q$, the spacetime maps onto four distinct geometric domains dictated by the surface gravity $κ|_{2M}$. We derive exact analytical expressions for the photon sphere radius $r_{\text{ph}}$ and its dynamic stability criterion, showing that external circular null orbits remain dynamically unstable across non-extremal regimes. Crucially, we prove that a stable photon sphere arises exclusively in the extremal configuration ($Q = -2M$), where it coincides precisely with the degenerate horizon ($r = 2M$). We argue that this horizon-bound stable photon orbit acts as an infinitely redshifted bound state for light and ultra-relativistic particles. Finally, we analyze the Bañados-Silk-West (BSW) effect for infalling timelike test particles, demonstrating that the center-of-mass energy $E_{\text{cm}}$ for critical collisions diverges as $E_{\text{cm}} \propto (r - r_h)^{-1/2}$ strictly at the extremal threshold $Q = -2M$.
