AI 中文总结
该研究在克尔黑洞背景下引入矢量暗物质浴，分离并求解扰动方程，发现黑洞周围形成特定密度尖峰，存在超辐射提取质量机制，还对比了标量场结果并讨论与超辐射不稳定性的混合。
AI 中文摘要
我们在克尔黑洞背景下考虑有质量矢量场扰动，固定黑洞引力影响球边缘处的场密度以模拟波冷暗物质浴，黑洞可从中持续吸积。我们采用Lunin、Frolov、Krtouš、Kubizňák和Santos的方法分离方程，结合解析与数值技术求解。我们发现该场在黑洞周围形成密度尖峰，剖面为$\rho \backsim r^{-3/2}$，与文献中研究的暗物质尖峰一致，除黑洞能层附近外，时空旋转未对其造成明显扭曲。对于任何非零自旋，会出现额外的超辐射 regime，其中共转模式从黑洞提取质量和角动量。我们发现，对于$10^9 M_\bigodot$的黑洞，超辐射 regime 中的质量提取率高达$10 M_\bigodot/\text{yr}$；对于大场质量，黑洞质量增长速率与史瓦西情况类似，$10^9 M_\bigodot$黑洞的该速率可达$\backsim 100 M_\bigodot/\text{yr}$。我们将这些结果与标量场对应结果进行比较，并讨论它们如何与超辐射不稳定性混合。
英文摘要
We consider a massive vector-field perturbation on a Kerr black hole background. We fix the field's density at the edge of the black hole sphere of influence to model a bath of wave cold dark matter, from which the black hole can accrete endlessly. We employ the approach of Lunin, Frolov, Krtouš, Kubizňák, and Santos to separate the equations, and solve them with a mix of analytical and numerical techniques. We find that the field forms a density spike around the black hole with profile $ρ\sim r^{-3/2}$, consistent with dark matter spikes studied in the literature, which is not significantly distorted by spacetime rotation, except near the black hole's ergoregion. For any nonzero spin, an additional superradiant regime appears, in which co-rotating modes extract mass and angular momentum from the black hole. We find a mass \textit{extraction} rate as high as $10\, M_\odot/\text{yr}$ in the superradiant regime for a $10^9\, M_\odot$ black hole. For large field masses, the rate at which the black-hole mass grows behaves similarly to the Schwarzschild case, reaching $\sim 100\, M_\odot/\text{yr}$ for a $10^9\, M_\odot$ black hole. We compare these results to their scalar-field counterparts and discuss how they mix with the superradiant instability.
Comments24 pages, 9 figures
