AI 中文总结
本文研究黑洞标量化中Ricci耦合的非线性完备化，推导近视界正则条件与分岔条件，发现稳定区域随γ增大而缩小，指数完备化比二次截断更受限。
AI 中文摘要
我们研究了标量-高斯-玻内特引力中静态、球对称黑洞的自发标量化，其中Ricci耦合为$F=1+\beta\phi^{2}/4+\gamma\beta^{2}\phi^{4}+O(\phi^{6})$，该耦合对二次耦合进行了非线性完备化。对于任意耦合和势，我们以闭式形式导出了近视界正则条件和视界曲率不变量；标量化分支在该条件退化处终止，此时视界曲率为有限值。弱非线性展开精确确定了分岔方向：对于无质量标量，其控制系数是$\beta$的二次函数，在$\beta=1.1156$处改变符号，并且与四次自相互作用线性相关。在标量场视界值相同的情况下，不同完备化在质量上的差异，至领头阶，与$\gamma$成正比。针对任意耦合的径向扰动主方程证实了在分岔点和转折点处稳定性的交换。因此，在所研究的范围内，随着$\gamma$增大，径向稳定的黑洞区域缩小；指数完备化对应的稳定区域小于二次截断对应的区域。
英文摘要
We study spontaneous scalarization of static, spherically symmetric black holes in scalar--Gauss--Bonnet gravity with a Ricci coupling $F=1 βϕ^{2}/4+γβ^{2}ϕ^{4}+O(ϕ^{6})$ that nonlinearly completes the quadratic one. For arbitrary couplings and potential, we derive the near-horizon regularity condition and horizon curvature invariants in closed form; scalarized branches terminate where this condition degenerates, at finite horizon curvature. A weakly nonlinear expansion fixes the bifurcation direction exactly: for a massless scalar, its governing coefficient is quadratic in $β$, changes sign at $β=1.1156$, and depends linearly on a quartic self-interaction. At equal horizon values of the scalar, completions differ in mass, to leading order, in proportion to $γ$. A radial-perturbation master equation for arbitrary couplings confirms the exchange of stability at the bifurcation and turning points. Consequently, the domain of radially stable black holes shrinks as $γ$ increases over the range studied; it is smaller for the exponential completion than for the quadratic truncation.
Comments39 pages, 2 figures
