质量膨胀或标量场刚性：度量 $f(R)$ 中的柯西视界
Mass inflation or scalaron rigidity: Cauchy horizons in metric f(R)
- Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências da Universidade de Lisboa（里斯本大学理学院太空科学与天体物理研究所）
- Faculdade de Ciências da Universidade de Lisboa（里斯本大学理学院）
- Universidad de La Frontera（拉弗龙特拉大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文建立双零框架分析度量f(R)引力中柯西视界动力学，区分质量膨胀与标量场抵消，证明有界质量需蓝移可积抑制，并给出高曲率渐近线性及标量场质量发散的局部刚性分类。
AI中文摘要：
我们为度量 $f(R)$ 引力中的柯西视界动力学建立了一个双零框架，该框架将普通质量膨胀与标量场抵消以及从蓝移不稳定性中真正逃逸区分开来。从精确的球对称霍金质量输运方程出发，我们证明，当有效纵向源最终非负、一致主导混合通道且具有发散蓝移加权积分时，规则的非退化柯西视界会发生质量膨胀。因此，有界质量需要该源被足够强的蓝移可积抑制，或存在独立的竞争通道。然后我们分析较弱的支路，其中标量场仅抵消领先的Price尾贡献。在非抵消横向和迹渐近条件下，这迫使 $|R|\to\infty$ 且理论在高曲率下渐近线性，$f(R)/R\to F_->0$，其中 $F_-\equiv\lim_{v\to\infty}f_R$。曲率系数由横向渐近显式确定。对于具有有限高曲率 $f_{RR}$ 极限的规则模型类，可得 $f_{RR}\to0$。更尖锐地，每个最终可行的 $f_{RR}>0$ 支路都被迫满足 $R\to-\infty$ 和 $\Lambda_\infty>-1$；标准标量场质量参数随后发散，而附加的可微性条件给出 $m_{\rm sc}^2\sim F/(3f_{RR})\to+\infty$。在爱因斯坦框架中，标量场的零类动贡献非负，因此约当框架中的抵消不能解释为负标量场零能量。结果是一个局部刚性分类，而非强宇宙审查的全局定理。
英文摘要：
We develop a double-null framework for Cauchy-horizon dynamics in metric $f(R)$ gravity that separates ordinary mass inflation from scalaron cancellation and genuine escape from the blueshift instability. Starting from the exact spherical Hawking-mass transport equation, we show that a regular nondegenerate Cauchy horizon undergoes mass inflation whenever the effective longitudinal source is eventually nonnegative, uniformly dominates the mixed channel, and has a divergent blueshift-weighted integral. Hence bounded mass requires sufficiently strong blueshift-integrable suppression of this source or an independent competing channel. We then analyze the weaker branch in which the scalaron cancels only the leading Price-tail contribution. Under non-cancelling transverse and trace asymptotics, this forces $|R|\to\infty$ and an asymptotically linear high-curvature theory, $f(R)/R\to F_->0$, where $F_-\equiv\lim_{v\to\infty}f_R$. The curvature coefficient is fixed explicitly by the transverse asymptotics. For regular model classes with a finite high-curvature $f_{RR}$ limit one obtains $f_{RR}\to0$. More sharply, every eventually viable branch with $f_{RR}>0$ is forced to $R\to-\infty$ and $Λ_\infty>-1$; the standard scalaron mass parameter then diverges, while an additional differentiable rate condition yields $m_{\rm sc}^2\sim F/(3f_{RR})\to+\infty$. In the Einstein frame the scalaron null kinetic contribution is nonnegative, so the Jordan-frame cancellation cannot be interpreted as negative scalaron null energy. The result is a local rigidity classification rather than a global theorem of strong cosmic censorship.
