蒸发黑洞中视界BMS戈德斯通模式的动力学选择

中文摘要 AI 辅助

我们研究蒸发的Vaidya-Schwarzschild黑洞时空中与近视界BMS超平移相关的视界软自由度的动力学。考虑超平移参数的动力学性质，我们直接从爱因斯坦-希尔伯特作用量推导其有效作用量。所得的戈德斯通 sector 本质上与演化的黑洞动力学耦合，质量函数参与戈德斯通模式的演化，而戈德斯通构型则对黑洞质量的动力学演化有贡献。方位角周期性和极点处的正则性选出物理上可容许的角向 sector，并给出依赖于质量的方位角模式选择定则。因此，视界支撑的戈德斯通模式的谱随黑洞质量演化；蒸发过程中视界收缩时，视界上留下的低阶模式数量逐渐减少。蒸发由此诱导了视界软 sector 的动力学滤波，该滤波本质上源于黑洞质量动力学。这些结果提供了一个有效的引力框架，将近视界BMS对称性、动力学戈德斯通模式与黑洞蒸发联系起来，表明宏观视界演化与视界上引力软自由度的微观组织之间存在直接关联。

英文摘要

We investigate the dynamics of horizon soft degrees of freedom associated with near-horizon BMS supertranslations in an evaporating Vaidya-Schwarzschild black hole spacetime. Considering the dynamic nature of the supertranslation parameter, we derive its effective action directly from the Einstein-Hilbert action. The resulting Goldstone sector is intrinsically coupled to the evolving black hole dynamics, with the mass function entering the evolution of the Goldstone modes while the Goldstone configuration contributes to the dynamical evolution of the black hole mass. Azimuthal periodicity and regularity at the poles select the physically admissible angular sector and yields a mass-dependent $selection\ rule$ on the azimuthal modes. Consequently, the spectrum of horizon-supported Goldstone modes evolves with the black hole mass; as the horizon shrinks during evaporation, the horizon is left with a progressively reduced set of lower-order modes. The evaporation thus induces a dynamical filtering of the horizon soft sector, arising intrinsically from the black hole mass dynamics. These results provide an effective gravitational framework linking near-horizon BMS symmetry, dynamical Goldstone modes, and black hole evaporation, suggesting a direct connection between macroscopic horizon evolution with the microscopic organization of the gravitational soft degrees of freedom residing on the horizon.

发表机构

• Indian Institute of Technology Guwahati（印度理工学院古瓦哈提分校）

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