发表机构
Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências da Universidade de Lisboa; Departamento de Física, Faculdade de Ciências da Universidade de Lisboa; Departamento de Ciencias Físicas, Universidad de La Frontera（里斯本大学理学院空间科学与天体物理研究所; 里斯本大学理学院物理系; 拉弗龙特拉大学物理科学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对f(R)引力，分离多尔戈夫-川崎不稳定性与强场视界动力学，利用勒让德势分析标量曲率子特性，结合赖斯纳-诺德斯特龙解验证恒等式，为相关引力问题提供分层框架。
AI 中文摘要
多尔戈夫-川崎不稳定性测试了度规f(R)引力中的局域标量曲率子响应，但未确定强场视界动力学。我们利用F=f_R和勒让德势𝒰(F)=FR-f将这些问题分离。标量曲率子恢复系数为m_sc²=(F-Rf_RR)/(3f_RR)，而精确的球形沃尔德面积输运恒等式抵消了标量曲率子海森矩阵。其爱因斯坦框架解释将纵向动能聚焦与依赖势的交叉聚焦区分开来。我们证明，在固定常曲率背景且物质无迹的情况下，输运仅依赖于(f,f_R)，而标量曲率子质量取决于可独立调节的f_RR。f(R)=R+αR²中的赖斯纳-诺德斯特龙解提供了一个精确判别器：相同的背景输运与相反的标量曲率子质量符号共存。一个具有变化F的带电解和宇宙学检验在该常F区域之外测试了这些恒等式。对于非退化柯西视界处传输的非零质量标量曲率子尾，条件固定背景估计给出了广义熵聚焦的不可积贡献。该估计未确立非线性质量暴胀或特定可延拓类。这些结果为耦合正则性、背景输运、标量曲率子稳定性和非线性内视界演化提供了分层框架。
英文摘要
The Dolgov-Kawasaki instability tests the local scalaron response in metric $f(R)$ gravity, but does not determine strong-field horizon dynamics. We separate these questions using $F=f_R$ and the Legendre potential $\mathcal U(F)=FR-f$. The scalaron restoring coefficient is $m_{\rm sc}^2=(F-Rf_{RR})/(3f_{RR})$, whereas exact spherical Wald-area transport identities cancel the scalaron Hessian. Their Einstein-frame interpretation distinguishes longitudinal kinetic focusing from potential-dependent cross-focusing. We prove that, at fixed constant-curvature background with tracefree matter, transport depends only on $(f,f_R)$, while the scalaron mass depends on the independently adjustable $f_{RR}$. Reissner-Nordström in $f(R)=R+αR^2$ gives an exact discriminator: identical background transport coexists with opposite scalaron mass signs. A charged solution with varying $F$ and a cosmological check test the identities beyond this constant-$F$ sector. For a nonzero massive scalaron tail transmitted to a nondegenerate Cauchy horizon, a conditional fixed-background estimate gives a nonintegrable contribution to generalized entropy focusing. This estimate does not establish nonlinear mass inflation or a particular extendibility class. The results provide a layered framework for coupling regularity, background transport, scalaron stability, and nonlinear inner-horizon evolution.
Comments16 pages
