General relativistic theory of charged accretion disk structures around black holes: influence of the (self)-electromagnetic interaction

在这个项目中，我们专注于吸积盘作为带电的完美流体。众所周知，电磁场对黑洞或中子星等致密物体周围的吸积盘的结构、物理和演化具有强烈的影响。由于黑洞无法直接观测，而且吸积盘可以非常接近中心致密物体，因此它们是强引力或近视界状态以及黑洞和中子星物理学的完美探测器。对吸积盘的全面分析必须包括各种背景和影响的组合。在由带电流体构成的吸积盘的情况下，盘的电荷对自身的影响似乎是一种不可避免的效应，这种效应仍然主要是未被探索的。对于这样复杂的问题，首先使用提供分析方法的理想化模型来研究情况是很自然的，这种分析方法在模型中提供了对物理机制的透彻了解。为了全面理解，必须进行广义相对论磁流体动力学模拟。我们的主要重点是吸积盘模拟的几何厚盘框架内的理想带电流体。我们将分三步进行：（i）我们将确定电磁自相互作用对圆盘的影响。首先，圆盘的电磁场将被描述为从圆盘中心的带电环发出并作用于圆盘。在一个逐次逼近的过程中，我们将确定整个圆盘的法拉第张量。我们将描述感生场对吸积盘性质的影响。(ii)研究了含自场的带电厚盘模型的振动性和稳定性。我们分析了振荡模式，并将其结果与高频准周期振荡的观测结果进行了比较。从应用微扰的二阶分析，然后我们将调查的各种带电厚平衡解的时间演化。(iii)最后，如果时间允许，我们将考虑一个玩具模型来再现由事件视界望远镜合作发布的M87中心的偏振图像。这个图像取决于磁场的几何形状和时空曲率。在所有情况下，我们试图找到精确或近似的解析解。在不可能的情况下，我们也将采用数值方法。

In this project, we focus on accretion disks as charged perfect fluids. Electromagnetic fields are well known to have a strong influence on the structure, physics and evolution of accretion disks around compact objects like black holes or neutron stars. Since black holes cannot be observed directly and since accretion disks can approach the central compact object very closely, they are a perfect probe of the strong gravity or near-horizon regime and of the physics of the black holes and neutron stars. A full analysis of accretion disks has to include a combination of a variety of settings and influences. In case of an accretion disk made of a charged fluid, the influence of the charge of the disk on itself appears as one of the inevitable effects which are still mainly unexplored. For such complex problems, it is natural to first study the situation using idealized models offering analytic approaches, which provide a -- within the model -- thorough insight into the physical mechanisms. For a complete understanding general relativistic magneto-hydrodynamical simulations have to be carried through. Our primary focus is on accretion disks modeled by an ideal charged fluid within the geometrically thick disk framework. We will proceed in three steps: (i) We will determine the influence of the electromagnetic self-interaction on the disk. To start with, the electromagnetic field of the disk will be described as emerging from a charged ring on the disk center and acting on the disk. In a successive approximation procedure, we will determine the Faraday tensor of the entire disk. We will describe the influence of the induced field on the properties of the accretion disk. (ii) We study the oscillations and stability of the charged thick disk model including the self-field determined in (i). We analyse the oscillation modes and compare that result with the observations of high frequency quasi-periodic oscillations. From second order analysis of applied perturbations, we then will investigate the temporal evolution of the various charged thick equilibrium solutions. (iii) Finally, if time permits, we will consider a toy model to reproduce the polarized image of the center of M87 released by the Event Horizon Telescope collaboration. This image depends, among many other effects, on the magnetic field geometry and the space-time curvature. In all cases we try to find exact or approximate analytic solutions. In cases where this is impossible we will also apply numerical methods.