黑洞与超轻暗物质之间的相互作用：解析解
Interplay between Black Holes and Ultralight Dark Matter: Analytic Solutions
AI总结：
本文用解析近似方法研究非旋转超大质量黑洞与超轻标量暗物质经典波的相互作用，推导黑洞“毛发”、动力学Love数、束缚态谱及中心孤子解，并可靠计算吸积率。
摘要：
暗物质（DM）可以由一种标量场构成，该标量场如此之轻，以至于星系晕中的暗物质粒子最好用经典波来描述。我们采用一种解析的（尽管是近似的）方法，研究这些经典解如何受到星系中心一个非旋转超大质量黑洞存在的影响。依靠这种解析控制，我们考察了在视界处施加通常被忽视的因果边界条件所带来的后果。首先，我们考察暗物质的反作用可以忽略的情形。标量场在大距离处按幂律衰减，从而赋予黑洞“毛发”。我们在很宽的参数范围内推导了场分布的解，包括暗物质旋转的情形。作为副产品，我们提取了标量微扰的动力学 Love 数。接下来，我们确定了束缚态的谱及其行为。最后，我们纳入标量场的自引力，重点关注暗物质在星系中心形成孤子（玻色星）的情形。我们推导了距中心任意距离处孤子的解析表达式。利用一个即使在视界尺度上仍然适用的解，我们能够可靠地计算黑洞的吸积率。
英文摘要：
Dark matter (DM) can consist of a scalar field so light that DM particles in the galactic halo are best described by classical waves. We investigate how these classical solutions are influenced by the presence of a non-rotating supermassive black hole at the center of the galaxy, using an analytical, albeit approximate, approach. Relying on this analytic control, we examine the consequences of imposing causal boundary conditions at the horizon, which are typically overlooked. First, we examine the scenario where the backreaction of dark matter can be neglected. The scalar field decays like a power law at large distances, thus endowing the black hole with "hair". We derive solutions for the field profile over a wide range of parameters, including cases with rotating dark matter. As a by-product, we extract the dynamical Love numbers for scalar perturbations. Next, we determine the spectrum of bound states and their behaviour. Finally, we incorporate the self-gravity of the scalar field, with a focus on the situation where dark matter forms a soliton (boson star) at the center of the galaxy. We derive an analytical expression for the soliton at every distance from the center. With a solution that remains applicable even at horizon scales, we can reliably compute the accretion rate of the black hole.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
