AI 中文总结
研究嵌入指数密度暗物质晕的类史瓦西黑洞，通过求解爱因斯坦方程获解析解。分析其时空特性，利用观测约束参数，探讨标量扰动和灰体边界，揭示晕对黑洞相关特性的影响，如移动光子球和阴影半径、影响准正则频率及灰体传输等。
AI 中文摘要
我们研究了一类嵌入指数球对称暗物质晕中的史瓦西黑洞，其由现象学密度分布\(\rho(r)=\rho_0 e^{-r/r_0}\)建模。通过求解静态、球对称时空的爱因斯坦方程，我们得到了一个关于消逝函数的解析解，在没有晕的情况下它简化为史瓦西时空，当中心黑洞质量消失时简化为规则的晕配置。两个晕参数\(\rho_0\)和\(r_0\)描述了暗物质分布的强度和径向范围。我们分析了所得时空的曲率结构、能量条件、阴影可观测量、标量准正则模和灰体边界。里奇标量和里奇平方在原点处保持有限，而克雷奇曼标量在存在黑洞质量时保留通常的中心潮汐奇点。满足弱、零和主导能量条件，而强能量条件在有限径向区间内被违反。我们还表明，晕单调地移动光子球和阴影半径，这使我们能够从M87*和Sgr A*的EHT观测中得出近似约束。对于标量扰动，帕德重整化WKB近似产生稳定的准正则频率，而标准WKB近似对于更高的泛音和强晕配置变得不可靠。最后，灰体边界表明晕削弱了通过有效势垒的传输，特别是在低频时。
英文摘要
We study a class of Schwarzschild black holes embedded in an exponential-spheroidal dark matter halo, modelled by a phenomenological density profile $ρ(r)=ρ_0 e^{-r/r_0}$. By solving the Einstein equations for a static, spherically symmetric spacetime, we obtain an analytic solution for the lapse function that reduces to the Schwarzschild spacetime in the absence of the halo and to a regular halo configuration when the central black hole mass vanishes. Indeed, the two halo parameters, $ρ_0$ and $r_0$, describe the strength and radial extent of the dark matter distribution. We analyse the curvature structure, energy conditions, shadow observables, scalar quasi-normal modes and grey-body bounds of the resulting spacetime. The Ricci scalar and the Ricci square remain finite at the origin, whilst the Kretschmann scalar retains the usual central tidal singularity in the presence of a black hole mass. The weak, null, and dominant energy conditions are satisfied, whilst the strong energy condition is violated on a finite radial interval. We also show that the halo monotonically shifts the photon sphere and the shadow radius, which allows us to derive approximate constraints from the EHT observations of M87* and Sgr A*. For scalar perturbations, the Padé-resummed WKB approximation yields stable quasinormal frequencies, while the standard WKB approximation becomes unreliable for higher overtones and strong-halo configurations. Finally, the greybody bounds indicate that the halo weakens transmission through the effective barrier, particularly at low frequencies.
Comments17 pages, 8 figures, 3 tables
