标题： 静止带电标量场可以有多短？ 显示英文标题

标题： How short can stationary charged scalar hair be?

摘要： 现在已经明确，带电旋转的Kerr-Newman黑洞可以支持由最小耦合的大量标场组成的束缚态带电物质构型。我们在这里证明，外部支持的静态带电标量构型{\it 不能}可以任意紧凑。特别是，对于由带电旋转近极端Kerr-Newman黑洞支持的线性化带电大质量标量场，我们推导出外部带电标量“云”有效长度的显著紧凑下限$(r_{\text{field}}-r_+)/(r_+-r_-)>1/s^2$[此处$r_{\text{field}}$是静态标量构型的径向峰值位置，$\{s\equiv J/M^2, r_{\pm}\}$分别是中心支撑Kerr-Newman黑洞的无量纲角动量和视界半径]。值得注意的是，这个下限是普遍的，即它独立于所支持的带电标量场的物理参数（固有质量、电荷和角动量）。 显示英文摘要

摘要： It is by now well established that charged rotating Kerr-Newman black holes can support bound-state charged matter configurations which are made of minimally coupled massive scalar fields. We here prove that the externally supported stationary charged scalar configurations {\it cannot} be arbitrarily compact. In particular, for linearized charged massive scalar fields supported by charged rotating near-extremal Kerr-Newman black holes, we derive the remarkably compact lower bound $(r_{\text{field}}-r_+)/(r_+-r_-)>1/s^2$ on the effective lengths of the external charged scalar `clouds' [here $r_{\text{field}}$ is the radial peak location of the stationary scalar configuration, and $\{s\equiv J/M^2, r_{\pm}\}$ are respectively the dimensionless angular momentum and the horizon radii of the central supporting Kerr-Newman black hole]. Remarkably, this lower bound is universal in the sense that it is independent of the physical parameters (proper mass, electric charge, and angular momentum) of the supported charged scalar fields.