General Relativistic theory of viscous accretion disks around Black Holes

在这个项目中，我们将研究黑洞周围吸积盘的相对论理论。吸积盘有其最内部稳定的圆形轨道，可以非常接近黑洞。因此，吸积盘是强引力体制的完美探测器。我们将用黑洞外部几何中具有粘性的相对论流体来模拟吸积盘。为此，我们将首先用两种互补的方法推导出吸积盘的运动方程：(I)从唯象梯度展开格式和(Ii)从广义相对论动力学理论。对于得到的有效的相对论流体动力学或流体理论运动方程，我们期望时空曲率的附加耦合超过特殊相对论流体动力学方程的最小耦合，并且可能对Steller黑洞附近的吸积盘产生一些影响。利用这个运动方程，我们将研究(A)吸积盘的形状和结构，(B)最内部稳定圆轨道的物理，(C)吸积盘的振荡动力学，(D)吸积速率，以及其他可观测的性质。计算的结果将与现有的观测结果进行比较。由于我们还将探索和测试强引力区，我们将不仅假设克尔时空为外部时空几何，而且还将形式主义应用于更一般的黑洞时空，以及广义引力理论的黑洞解。

In this project we will study the relativistic theory of accretion disks around Black Holes. With their innermost stable circular orbits accretion disks can approach Black Holes very closely. Thus, accretion disks are a perfect probe of the strong gravity regime. We will model accretion disks by relativistic fluids with viscosity in the external geometry of a Black Hole. For that we first will derive the equations of motion for the accretion disks with two complementary methods: (i) from the phenomenological gradient expansion scheme and (ii) from the general relativistic kinetic theory. For the resulting effective relativistic hydrodynamical or fluid theoretical equations of motion we expect additional couplings to space-time curvature which are beyond the minimal coupling of the special relativistic hydrodynamical equations and which may have some influence on the accretion disk near to steller Black Holes. Using this equation of motion we then will investigate (a) the form and structure of the accretion disks, (b) the physics of the innermost stable circular orbits, (c) the oscillatory dynamics of accretion disks, and (d) the accretion rate, and other observable properties. The results of the calculations will be compared with available observations. Since we also will explore and test the strong gravity regime we will not only assume the Kerr space-time as external space-time geometry, but apply the formalism also to more general Black Hole space-times and also to Black Hole solutions of generalized theories of gravity.