发表机构
De La Salle University（德拉萨大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究复准正则频率对静态球对称黑洞几何与热力学的参数化，通过特定比率重建参数和尺度，计算有限多极误差，表明该构造是模型依赖逆过程，应用于引力波观测需更多微扰扇区。
AI 中文摘要
我们研究了一个复准正则频率如何参数化规定的静态、球对称黑洞族的几何结构和模型条件热力学。对于程函极限下的最小耦合无质量测试标量，比率\(\chi=\omega_R\tau=\omega_R/\omega_I = 2Q\)消除了整体质量尺度。若\(\chi\)在一个无量纲参数中是单射的，则该参数和几何尺度可在所选族内重建。归一化度规确定视界和霍金温度，而瓦尔德熵需要引力作用。对于RN形式族，\(\chi\)确定\(u = q^2\)但不确定电荷符号。常耦合静态MOG度规在\(\mathcal M=(1+\alpha)m_{\rm MOG}\)和\(u=\alpha/(1+\alpha)\)下精确为RN；因此，每个多极和泛音在映射背景上的完整最小耦合标量谱相同。两种赋值温度相等但与作用相关的熵不同。切比雪夫和WKB - 帕德计算量化了有限多极误差，在测试的\(l = 2\) RN网格上最大程函比率误差为\(2.1\times10^{-3}\)。该构造是模型依赖的逆过程，而非理论选择器。将其应用于引力波观测需要超出测试场程函近似的适当张量、矢量和标量微扰扇区。
英文摘要
We examine whether scalar eikonal quasinormal-mode data determine black-hole thermodynamics. For static, spherically symmetric, asymptotically flat, nonextremal geometries, we prove that the formal fixed-overtone expansion of a neutral, minimally coupled, massless scalar through order $L^{-N}$ depends only on the $(2N+2)$ jet of the lapse at the unstable photon sphere. For every finite $N$, real-analytic deformations can preserve this jet and the asymptotic Reissner--Nordström coefficients while changing the surface gravity and Hawking temperature. We also construct a nonanalytic $C^\infty$ deformation that is flat at the photon sphere. This deformation preserves the complete formal eikonal series to every algebraic order but changes the horizon position, temperature, and Einstein area entropy. A nonempty charged subfamily satisfies the weak energy condition as an effective Einstein source. Together, these four results establish the new finite-jet and all-orders thermodynamic obstruction. To separate geometric information from action-dependent information, we incorporate a previously established Reissner--Nordström--MOG comparison. The mapped backgrounds have identical normalized metrics, neutral-scalar boundary-value problems, exact scalar spectra, and Hawking temperatures, yet their Wald entropies differ because their curvature couplings differ. The resulting hierarchy shows that local photon-sphere data do not determine horizon thermodynamics and that even exact action-blind scalar data do not determine gravitational entropy. Agreement of the formal eikonal expansions for the deformed metrics does not imply exact finite-$\ell$ isospectrality. Global differences may appear beyond every algebraic order. Thermodynamic reconstruction from eikonal ringdown is therefore conditional on assumptions about the global metric and the gravitational action.
Comments2 figures, 21 pages
