Complexity Growth in Black Holes: A Comparison of the Volume and Action Proposals
黑洞中的复杂度增长:体积与作用量方案的比较
Suraj Maurya, Sashideep Gutti, Rahul Nigam, Swastik Bhattacharya
AI总结 通过比较CV和CA方案,研究BTZ、史瓦西、Reissner-Nordström和Kerr黑洞的复杂度晚期增长,发现CA方案在所有黑洞中给出普适的热力学标度,而CV方案依赖几何。
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在本文中,我们研究了通过复杂度-体积(CV)和复杂度-作用量(CA)方案定义的BTZ、史瓦西、Reissner-Nordström和Kerr黑洞的全息复杂度晚期增长。将先前的分析扩展到渐近AdS时空之外,我们包括了渐近平直几何,并采用CV和CA方案作为黑洞内部动力学的比较几何诊断。在所有考虑的情况下,复杂度增长率由视界热力学数据支配,并与$T_H S_H$成比例。虽然CV方案表现出依赖于几何的比例常数,但CA方案在所有研究的黑洞(包括非AdS情况)中给出了普适的热力学标度。我们进一步分析了在彭罗斯过程、超辐射和粒子吸积等物理过程中复杂度增长率的变化$\delta \dot{\mathcal{C}}$。我们发现$\delta \dot{\mathcal{C}}$表现出非平凡行为:在彭罗斯过程和超辐射下增加,而在粒子吸积下,根据下落粒子的角动量,它可以增加、保持不变或减少。在准平衡状态下,复杂度的变化紧密跟踪视界面积和内部体积增长的行为,而非平衡过程使其对角动量转移敏感,并可能在平衡近似下导致负值。这种行为突出了基于平衡处理的局限性,并促使进行包含视界应力和瞬态毛发的完全动力学分析。
In this article, we investigate the late-time growth of holographic complexity, defined via the complexity-volume (CV) and complexity-action (CA) prescriptions, for BTZ, Schwarzschild, Reissner-Nordström, and Kerr black holes. Extending previous analyses beyond asymptotically AdS spacetimes, we include asymptotically flat geometries and employ the CV and CA prescriptions as comparative geometric diagnostics of black hole interior dynamics. In all cases considered, the complexity growth rate is governed by horizon thermodynamic data and scales with $T_H S_H$. While the CV prescription exhibits geometry-dependent proportionality constants, the CA prescription yields a universal thermodynamic scaling across all black holes studied, including non-AdS cases. We further analyze variations in the complexity growth rate, $δ\dot{\mathcal{C}}$, under physical processes such as the Penrose process, superradiance, and particle accretion. We find that $δ\dot{\mathcal{C}}$ exhibits non-trivial behavior: it increases under the Penrose process and superradiance, while under particle accretion it can increase, remain unchanged, or decrease depending on the angular momentum of the infalling particle. In quasi-equilibrium regimes, the variation in complexity closely tracks the behavior of the horizon area and interior volume growth, whereas out-of-equilibrium processes render it sensitive to angular momentum transfer and may lead to negative values within an equilibrium approximation. This behavior highlights the limitations of equilibrium-based treatments and motivates a fully dynamical analysis incorporating horizon stresses and transient hair.