高维f(R)引力中黑洞解的涌现真空与稳定性约束
Emergent vacua and stability constraints on black hole solutions in higher-dimensional $f(R)$ gravity
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中文总结 AI 辅助
该研究探讨高维f(R)引力的黑洞解，发现五维中纯R²修正无法动态生成稳定宇宙学常数，单一项曲率修正需满足n>D/2，多阶多项式修正可突破限制实现全局稳定真空时空。
中文摘要 AI 辅助
我们研究高维f(R)引力中的静态球对称真空解，以由作用量$f(R)=R+\alpha R^2-2\Lambda$描述的五维Starobinsky模型为起点。通过在常标量曲率时空上施加无鬼稳定性判据$f'(R)>0$，我们证明在五维中无法仅由纯$R^2$几何修正动态生成稳定的有效宇宙学常数；其存在与裸宇宙学常数密不可分。将该分析推广到任意维度$D$及裸宇宙学常数为零的单一项曲率修正$f(R)=R+\alpha R^n$，我们导出了稳定涌现真空存在所需的普适稳定性界$n>D/2$。最后，我们证明将引力作用量扩展为多项多项式层级可规避这一严格限制。通过包含$\mathcal{O}(R^3)$阶的曲率修正，扩展的几何自由度同时满足迹约束和稳定性判据。此外，我们确定了精确的参数空间边界，确保不仅渐近真空稳定，且严格全局稳定（对所有$R$有$f'(R)>0$），从而能在$D\geq5$时仅从高阶几何项动态生成精确、全局无鬼的真空时空。在我们的分析中未完全施加标量质量要求$m_s^2>0$，对其在本研究考虑的模型上的含义的详细研究留待未来工作。
英文摘要
We investigate static spherically symmetric vacuum solutions in higher-dimensional $f(R)$ gravity, beginning with the five-dimensional Starobinsky model governed by the action $f(R) = R + αR^2 - 2Λ$. By enforcing the ghost-free stability criterion $f'(R) > 0$ on constant scalar curvature spacetimes, we show that a stable effective cosmological constant cannot be dynamically generated from pure $R^2$ geometric corrections in five dimensions; its existence is inextricably tied to a bare cosmological constant. Generalizing this analysis to arbitrary dimensions $D$ and single-term curvature corrections $f(R) = R + αR^n$ with a vanishing bare cosmological constant, we derive a universal stability bound, $n > D/2$, required for the existence of stable emergent vacua. Finally, we demonstrate that expanding the gravitational action to a multi-term polynomial hierarchy circumvents this strict limitation. By including curvature corrections up to $\mathcal{O}(R^3)$, the extended geometric degrees of freedom simultaneously satisfy the trace constraint and the stability criterion. Furthermore, we establish the exact parameter space boundaries that ensure not only asymptotic vacuum stability but strict global stability ($f'(R) > 0$ for all $R$), allowing for the dynamical generation of exact, globally ghost-free vacuum spacetimes in $D \ge 5$ purely from higher-order geometric terms. The scalaron mass requirement, $m_s^2>0$ is not imposed in full in our analysis. A detailed investigation of its implications on the models considered in this work are left for future study.
