作为广义相对论检验的黑洞图像：时空几何的影响
Black Hole Images as Tests of General Relativity: Effects of Spacetime Geometry
摘要：
超大质量黑洞的图像被光学薄的、辐射效率低的吸积流所包围，就像用事件视界望远镜观察到的那样，其特征是黑洞阴影周围有一个明亮的发射环。在克尔时空中，这个明亮的环，当狭窄时，紧密地跟踪阴影的边界，并且可以通过适当的校准作为它的代理。本文通过考虑两种特殊的时空几何来扩展这一说法的有效性：一种是修正引力理论的场方程的解，另一种是参数偏离克尔但当其偏离参数消失时恢复克尔时空的解。一个协变的，轴对称的分析模型的吸积流守恒定律的基础上，跨越了广泛的等离子体条件的计算合成的非克尔黑洞图像，然后进行分析和表征。我们发现在所有时空中：（i）在确定黑洞图像中观察到的环的直径时，起关键作用的是引力透镜不稳定光子轨道，而不是事件视界或最里面的稳定圆形轨道，（ii）这些图像中的亮环的大小与黑洞阴影的边界成比例，并包围黑洞阴影的边界，即使在明显偏离克尔时，以及（iii）吸积等离子体的物理性质的不确定性对图像的直径和黑洞阴影的直径之间的关系引入次优势修正。这些结果为利用黑洞图像探测和检验超大质量黑洞的时空提供了新的理论依据。
英文摘要：
The images of supermassive black holes surrounded by optically-thin, radiatively-inefficient accretion flows, like those observed with the Event Horizon Telescope, are characterized by a bright ring of emission surrounding the black-hole shadow. In the Kerr spacetime this bright ring, when narrow, closely traces the boundary of the shadow and can, with appropriate calibration, serve as its proxy. The present paper expands the validity of this statement by considering two particular spacetime geometries: a solution to the field equations of a modified gravity theory and another that parametrically deviates from Kerr but recovers the Kerr spacetime when its deviation parameters vanish. A covariant, axisymmetric analytic model of the accretion flow based on conservation laws and spanning a broad range of plasma conditions is utilized to calculate synthetic non-Kerr black-hole images, which are then analysed and characterized. We find that in all spacetimes: (i) it is the gravitationally-lensed unstable photon orbit that plays the critical role in establishing the diameter of the rings observed in black-hole images, not the event horizon or the innermost stable circular orbit, (ii) bright rings in these images scale in size with, and encompass, the boundaries of the black-hole shadows, even when deviating significantly from Kerr, and (iii) uncertainties in the physical properties of the accreting plasma introduce subdominant corrections to the relation between the diameter of the image and the diameter of the black-hole shadow. These results provide important new theoretical justification for using black-hole images to probe and test the spacetimes of supermassive black holes.
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