稳定额外维度量连续景观
Continuum Landscape of stable extra-dimensional metrics
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中文总结 AI 辅助
研究含二次曲率项的修正引力中额外维稳定度量，发现稳定解形成连续景观，并影响四维参数，且局域扰动无法引发状态间转变。
中文摘要 AI 辅助
我们研究了带有二次曲率项（$R^2$、$R_{AB}R^{AB}$ 和 $R_{ABCD}R^{ABCD}$）的修正引力。在此框架下，额外维的几何由高维场方程连同辅助条件决定。对于非均匀度量，我们推导了在辐射子激发下的新稳定性条件。核心结果是，满足这些条件的稳定解并非孤立：一个典型的稳定正则度量在其紧邻邻域内属于一个连续族的稳定度量。由于有效的四维物理参数依赖于额外维几何，这种稳定度量的几何景观诱导出有效的四维参数的连续景观。景观内不同静态解之间的转变不能由空间局域扰动引起，因为其渐近衰减（$|x|\to\infty$）保留了区分这些状态的边界数据。我们还注意到从双膜到单膜构型的可能拓扑转变，这与度量函数 $r(u)$ 的正则零点数量的变化相关。
英文摘要
We investigate modified gravity with quadratic curvature terms ($R^2$, $R_{AB}R^{AB}$, and $R_{ABCD}R^{ABCD}$). In this framework, the geometry of the extra dimensions is determined by the higher-dimensional field equations together with auxiliary conditions. For inhomogeneous metrics, we derive new stability conditions under radion excitations. The central result is that stable solutions satisfying these conditions are not isolated: a typical stable regular metric belongs to a continuous family of stable metrics in its immediate neighbourhood. Since the effective four-dimensional physical parameters depend on the extra-dimensional geometry, this geometrical landscape of stable metrics induces a continuous landscape of effective four-dimensional parameters. Transitions between distinct static solutions within the landscape cannot be induced by spatially localized perturbations, whose asymptotic decay ($|x|\to\infty$) preserves the boundary data distinguishing the states. We also note a possible topological transition from a two-brane to a one-brane configuration, associated with a change in the number of regular zeros of the metric function $r(u)$.
发表机构
- National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)（国立核研究大学莫斯科工程物理学院）
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