稳态标量云、似正模振铃与（近）极端旋转Kalb-Ramond黑洞的观测特征：从超辐射阈值到EHT约束
Stationary scalar clouds, quasinormal ringing, and observational signatures of (near-)extremal rotating Kalb-Ramond black holes: from the superradiant threshold to EHT bounds
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中文总结 AI 辅助
该研究针对（近）极端旋转Kalb-Ramond黑洞的有质量标量场，解析其方程分离特性、稳态共振与似正模分支，计算超辐射、引力透镜与阴影特征，并结合EHT观测给出更严格的洛伦兹破缺参数约束。
中文摘要 AI 辅助
我们研究了Kumar、Ghosh和Wang提出的旋转Kalb-Ramond黑洞在其三参数族$(a,γ,λ)$的（近）极端区域上的有质量标量场。通过直接代入验证，Klein-Gordon-Fock方程在该背景下可分离，径向与角向分离常数满足关系$Λ_{rad}=Λ_{ang}+a^2ω^2-2amω$。在严格极端条件下，视界多项式与函数$K(r)$存在公共零点，使得$K^2/Δ$在该处正则，并将径向问题在Kerr线$(γ=0)$和Kerr-Newman线$(λ=1)$上简化为Whittaker形式。稳态共振满足$ω=mΩ_H$且符合束缚态条件$μ>mΩ_H$，高次谐波从上方在阈值处累积；在纯Kalb-Ramond内部区域，我们将精确径向方程作为两点边值问题求解。偏离极端性后，标量云延续到共转零阻尼分支$ω_n=mΩ_H-iκ(n+1/2+β)$，由相同的近视界指数$β$主导；光子球族是另一个可观测的 distinct 特征。通过直接积分得到灰体因子和超辐射放大，恢复了Kerr黑洞上的经典标量放大效应。强引力透镜在Bozza-Tsukamoto极限下处理，考虑两种旋转方向的光子轨道，其中顺行对数系数与Schwarzschild值存在显著偏离。阴影轮廓由Carter-Hamilton-Jacobi分离得到。将标量云存在区域与Zubair、Raza和Maqsood的事件视界望远镜（EHT）观测窗口交叉，得到的洛伦兹破缺参数$(γ,λ)$约束比单独任一约束更严格。
英文摘要
We study a massive scalar field on the rotating Kalb-Ramond black hole of Kumar, Ghosh and Wang, in the (near-)extremal corner of its three-parameter family $(a,γ,λ)$. We verify by direct substitution that the Klein-Gordon-Fock equation separates on this background, with radial and angular separation constants related by $Λ_{rad}=Λ_{ang}+a^2ω^2-2amω$. At exact extremality the horizon polynomial and the function $K(r)$ share a zero, rendering $K^2/Δ$ regular there and reducing the radial problem to Whittaker form on the Kerr line $(γ=0)$ and the Kerr-Newman line $(λ=1)$. The stationary resonances saturate $ω=mΩ_H$ and satisfy the bound-state condition $μ>mΩ_H$, with overtones accumulating at the threshold from above; in the genuinely Kalb-Ramond interior we solve the exact radial equation as a two-point boundary value problem. Moving off extremality, the clouds continue onto the co-rotating zero-damped branch $ω_n=mΩ_H-iκ(n+1/2+β)$, governed by the same near-horizon exponent $β$; the photon-sphere family is a distinct observable. Greybody factors and superradiant amplification are obtained by direct integration, recovering the classical scalar amplification on Kerr. Strong-field lensing is treated in the Bozza-Tsukamoto limit with rotating photon orbits of both senses, where the prograde logarithmic coefficient departs strongly from its Schwarzschild value. The shadow contour follows from the Carter-Hamilton-Jacobi separation. Crossing the Event Horizon Telescope window of Zubair, Raza and Maqsood with the cloud-existence region yields a narrower bound on the Lorentz-violating parameters $(γ,λ)$ than either constraint alone.
