General relativistic theory of spin-fluid accretion disks around Black Holes

由于吸积盘可以非常接近黑洞，它们是研究强引力或近视界区的重要工具。吸积盘的行为取决于构成吸积盘的材料以及时空几何。通常吸积盘是由一个理想的流体与质量密度和压力或-为了考虑吸积过程-与粘度。还讨论了带电流体或等离子体。由于星际物质-特别是在强引力区域-可能由原子或基本粒子组成，因此可以想象，这些原子或亚原子成分的自旋或磁矩也可能在吸积盘的行为中发挥作用。因此，本建议讨论自旋流体作为吸积盘的物质模型。与通常假设的物质模型相比，这里的自旋与时空曲率和外部电磁场的额外耦合，例如，星系起源将存在，并可能影响磁盘的物理特性。自旋也提供了一个首选的工具来寻找一个假设的时空扭曲。除此之外，自旋流体还要求专门研究运动方程的双曲性，从而研究因果关系。另一个方面是需要实施补充自旋条件，这可能会影响运动方程，从而也影响双曲性。这些性质也可能依赖于假设挠率的存在。这个项目的最终目的是计算吸积盘的物理性质，即它的形状，密度分布，振荡和其他特征。

Since accretion disks can approach Black Holes very closely they are an important tool to investigate the strong gravity or the near horizon regime. The behavior of accretion disks depends on the material the disks is made of as well as on the space-time geometry. Usually accretions disks are modeled either by an ideal fluid with mass density and pressure or -- in order to account for the accretion process -- with viscosity. Also charged fluids or plasma have been discussed. Since interstellar matter -- in particular in strong gravity regions -- may consist of atoms or elementary particles it might be conceivable that also the spin or the magnetic moment of these atomic or sub-atomic constituents may play a role in the behavior of accretion disks. Accordingly, the present proposal discusses spin fluids as matter model for accretion disks. Compared with the usually assumed matter models, here additional couplings of the spin to the space-time curvature and to external electromagnetic fields of, e.g., galactic origin will be present and probably influence the physical properties of the disk. Spin also offers a preferred tool to search for a hypothetical space-time torsion. Beside that, spin fluids also ask for dedicated studies of the hyperbolicity of the equations of motion and, consequently, of causality. A further aspect is the need to implement supplementary spin conditions which may influence the equations of motion and, thus, also the hyperbolicity. These properties may also depend on the existence of a hypothetical torsion. The final aim of this project then is to calculate the physical properties of accretion disk, that is, its shape, the density profile, oscillations, and other characteristics.