AI 中文总结
本文针对Sgr A*与M87*周围的暗物质尖峰，提出一种非标准势实标量场模型，通过逆向设计运动方程得到符合要求的势，该模型可检验且能用于研究含尖峰黑洞的引力扰动及反作用。
AI 中文摘要
理论模型表明，沉浸在暗物质中的黑洞的绝热增长可导致黑洞事件视界附近形成高密度暗物质区域，即“尖峰”。这些尖峰的密度在理论和观测上由幂律形式ρ(r) ∝ r^(-γ_sp)决定。已有研究表明，该尖峰可能对中心黑洞发出的引力波和阴影半径产生可探测的影响。本研究采用具有非标准势的实标量场来建模暗物质尖峰，更具体地说，我们“逆向设计”运动方程，以找到一种标量场的势，该势允许具有所需能量密度和合理背景几何的运动方程解。我们表明，由此产生的几何是可检验的。此外，该解源自协变作用量这一事实，使得研究存在尖峰时黑洞的引力扰动成为可能，包括尖峰的反作用。
英文摘要
Theoretical models suggest that the adiabatic growth of a black hole immersed in dark matter can lead to the formation of high density regions of dark matter, known as ``spikes'', near the black hole event horizon. The density of these spikes is determined theoretically and observationally to be a power law of the form $ρ(r) \propto r^{-γ_\text{sp}}$. It has been shown that the spike can potentially have a detectable impact on the emitted gravitational waves and shadow radius of the central black hole. In this work, we model the dark matter spike using a real scalar field with a non-standard potential. More specifically we ``reverse engineer'' the equations of motion to find a potential for the scalar field that permits a solution to the equations of motion with desired energy density and reasonable background geometry. We show that the emerging geometry is testable. In addition, the fact that the solution is derived from a covariant action makes it possible to study gravitational perturbations of the black hole in the presence of a spike including the backreaction of the spike.
Comments23 pages, 6 figures, regular article
