Propagation of light signals near a black hole surrounded by a plasma

30年前，黑洞只是爱因斯坦广义相对论所允许的假设对象，而我们现在有强有力的观测证据表明它们确实存在于自然界中。我们所能获得的关于黑洞的信息主要来自它对靠近黑洞的光信号（包括光谱以外的信号）的影响。在这个项目中，我们计划研究两个这样的效果，考虑光传播不仅在真空中，而且在等离子体是相关的无线电信号。(a)首先，我们要计算从围绕黑洞运行的脉冲星发出的信号的旅行时间。与早期对这个问题的研究相反，我们想把围绕黑洞的不均匀等离子体的影响考虑在内。(b)其次，我们想考虑来自一个（小但扩展的）光源的光，该光源围绕黑洞运行，并在其静止坐标系中各向同性地发射。这个光源可以解释为吸积盘中的一个热点。 特别地，我们要考虑光源绕其轴旋转的情况，并且要考虑旋转对所发射的辐射的影响。在对光在真空中的传播做了这些之后，我们还想考虑不均匀等离子体的影响。这有有趣的应用，即使是在源不旋转的情况下：将黑洞周围的辐射旋转盘建模为由许多轨道光源组成，可以计算等离子体对这种盘的视觉外观的影响。在所有情况下，我们的目标是尽可能导出精确的解析公式，否则使用解析近似方法。黑洞主要是由史瓦西或克尔时空模型，但其他度量（替代理论的黑洞和黑洞冒充者，如虫洞）也将部分包括在研究中。这个项目的主要动机来自于已经存在或预期的（超大质量或恒星）黑洞观测。等离子体对轨道光源辐射影响的解析公式将是评估这些观测结果并正确解释它们的重要工具。

Whereas 30 years ago black holes were just hypothetical objects allowed by Einstein's theory of general relativity, we have now strong observational evidence that they actually exist in Nature. The information we can get about a black hole comes mainly from its effects on light signals (including signals beyond the optical spectrum) that come close to the black hole. In this project we are planning to investigate two such effects, considering light propagation not only in vacuo but also in a plasma which is of relevance for radio signals. (a) Firstly we want to calculate the travel times of signals from a pulsar that orbits a black hole. In contrast to earlier studies of this problem we want to take the effects of an inhomogeneous plasma into account that surrounds the black hole. (b) Secondly we want to consider light from a (small but extended) source that orbits a black hole and emits isotropically in its rest frame. The light source may be interpreted as a hot spot in an accretion disc. In particular, we want to consider the case that the light source is spinning about its axis and the influence of the spin on the emitted radiation is to be taken into account. After doing this for light propagation in a vacuum, we also want to take the effects of an inhomogeneous plasma into account. This has interesting applications, even for the case that the source is non-spinning: Modelling a radiating rotating disc around a black hole as consisting of many orbiting light sources allows to calculate the influence of a plasma on the visual appearance of such a disc. In all cases, it is our goal to derive exact analytical formulas as far as possible and to use analytical apporoximation methods otherwise. The black hole is mainly to be modelled by the Schwarzschild or the Kerr spacetime, but other metrics (black holes of alternative theories and black hole impostors like wormholes) will be partly included in the investigation as well. A main motivation for this project comes from already existing or expectable observations of (supermassive or stellar) black holes. Analytic formulas for the influence of a plasma on the radiation emitted by orbiting light sources would be important tools for evaluating these observations and interpreting them correctly.