发表机构
Hanoi Pedagogical University 2（河内第二师范大學）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究证明规则黑洞内视界表面引力在折叠点按(M-M_crit)^{1/2}标度，并基于此构建现象学级联闭合，给出质量间隙衰减律及有效绝热模型，区分推导与假设。
AI 中文摘要
对规则黑洞的半经典分析表明，内视界不稳定性可以驱动俘获区以比霍金时间更快的速度蒸发，并催生一个瞬态的反俘获区。这种情况是否会重复成级联并终止于无视界构型，需要半经典爱因斯坦方程的自洽解，我们并未尝试求解。相反，在静态巴丁族内，我们表明Arrechea、Liberati和Spadafora（arXiv:2608.03538）的重整化应力张量（RSET）结果本身并不强制任何在近极端情形下假设级联的阻尼，因为其在固定周期持续时间的近极端极限是有限且非零的。然后，我们在任何其视界在折叠点合并的静态度规族的显式非退化假设下证明，内视界表面引力按|kappa_-| ~ (M-M_crit)^{1/2}标度，并在两个规则黑洞族（巴丁和海沃德）中验证了这一点，并带有量化的系统不确定性。基于此标度的现象学闭合给出质量间隙按x_n ~ n^{-2}衰减，对于折叠指数p和未校准的闭合指数q，推广为x_n ~ n^{-1/(pq)}；所需的循环次数是闭合的性质，而非物理预测。作为单独练习，我们从匹配所引RSET通量的广义Vaidya-Bardeen试探解的精确爱因斯坦张量构建了外视界质量的有效绝热模型；所得定律包含一个在朴素Schwarzschild-Vaidya关系中缺失的O(1)修正，仅渐近地松弛到M_crit，并在远离极端情形时给出比内视界放大时间尺度短至四个数量级的时间尺度，但在非常接近极端情形时则更长。我们区分了在所述假设下推导出的内容与闭合仅假设的内容。
英文摘要
Semiclassical analyses of regular black holes suggest that inner-horizon instabilities can drive the trapped region to evaporate faster than the Hawking time and seed a transient anti-trapped region. Whether this repeats into a cascade terminating in a horizon-free configuration requires a self-consistent solution of the semiclassical Einstein equations, which we do not attempt. Instead, within the static Bardeen family, we show that the renormalized-stress-tensor (RSET) result of Arrechea, Liberati and Spadafora (arXiv:2608.03538) does not by itself force any damping of a hypothetical cascade near extremality, since its near-extremal limit at fixed cycle duration is finite and nonzero. We then prove, under explicit nondegeneracy hypotheses on any static metric family whose horizons merge at a fold point, that the inner-horizon surface gravity scales as |kappa_-| ~ (M-M_crit)^{1/2}, and verify this in two regular black hole families, Bardeen and Hayward, with a quantified systematic uncertainty. A phenomenological closure built on this scaling gives a mass gap decaying as x_n ~ n^{-2}, generalizing to x_n ~ n^{-1/(pq)} for a fold exponent p and an uncalibrated closure exponent q; the required cycle count is a property of the closure, not a physical prediction. As a separate exercise, we build an effective adiabatic model for the outer-horizon mass from the exact Einstein tensor of a generalized Vaidya-Bardeen ansatz matched to the cited RSET flux; the resulting law includes an O(1) correction absent from the naive Schwarzschild-Vaidya relation, relaxes to M_crit only asymptotically, and gives a timescale shorter than the inner-horizon amplification timescale by up to four orders of magnitude away from extremality but longer very close to extremality. We distinguish what is derived under stated assumptions from what the closure simply postulates.
Comments13 pages, 7 figures
