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域的重要工具。吸积盘的行为取决于构成吸积盘的物质以及时空几何结构。通常，吸积盘要么用具有质量密度和压力的理想流体来模拟，要么--为了解释吸积过程--用粘性来模拟。还讨论了带电液体或等离子体。由于星际物质--特别是在强重力区域--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，本提案讨论了自旋流体作为吸积盘的物质模型。与通常假定的物质模型相比，这里将存在自旋与时空曲率和外部电磁场(例如银河系起源)的额外耦合，并可能影响盘的物理性质。Spin还提供了一种首选工具来搜索假设的时空扭曲。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的自旋条件，这可能会影响运动方程，从而也会影响双曲性。这些性质也可能取决于假设扭转的存在。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.