According to the no-hair theorem, all astrophysical black holes are fully
described by their masses and spins. This theorem can be tested observationally
by measuring (at least) three different multipole moments of the spacetimes of
black holes. In this paper, we analyze images of black holes within a framework
that allows us to calculate observables in the electromagnetic spectrum as a
function of the mass, spin, and, independently, the quadrupole moment of a
black hole. We show that a deviation of the quadrupole moment from the expected
Kerr value leads to images of black holes that are either prolate or oblate
depending on the sign and magnitude of the deviation. In addition, there is a
ring-like structure around the black-hole shadow with a diameter of about 10
black-hole masses that is substantially brighter than the image of the
underlying accretion flow and that is independent of the astrophysical details
of accretion flow models. We show that the shape of this ring depends directly
on the mass, spin, and quadrupole moment of the black hole and can be used for
an independent measurement of all three parameters. In particular, we
demonstrate that this ring is highly circular for a Kerr black hole with a spin
a<0.9M, independent of the observer's inclination, but becomes elliptical and
asymmetric if the no-hair theorem is violated. Near-future very-long baseline
interferometric observations of Sgr A* will image this ring and may allow for
an observational test of the no-hair theorem.

本文通过研究黑洞的电磁波谱观测结果，分析黑洞的形态，并且基于黑洞的质量、自旋及其四极矩的独立性，提出了独立测量三者的方法，此方法可以用于观测黑洞多重极矩、形态等是否符合无发定理。

用电磁波谱观测检验无毛定理：II. 黑洞影像

Testing the No-Hair Theorem with Observations in the Electromagnetic  Spectrum: II. Black-Hole Images

According to the no-hair theorem, an astrophysical black hole is uniquely
described by only two quantities, the mass and the spin. In this series of
papers, we investigate a framework for testing the no-hair theorem with
observations of black holes in the electromagnetic spectrum. We formulate our
approach in terms of a parametric spacetime which contains a quadrupole moment
that is independent of both mass and spin. If the no-hair theorem is correct,
then any deviation of the black-hole quadrupole moment from its Kerr value has
to be zero. We analyze in detail the properties of this quasi-Kerr spacetime
that are critical to interpreting observations of black holes and demonstrate
their dependence on the spin and quadrupole moment. In particular, we show that
the location of the innermost stable circular orbit and the gravitational
lensing experienced by photons are affected significantly at even modest
deviations of the quadrupole moment from the value predicted by the no-hair
theorem. We argue that observations of black-hole images, of relativistically
broadened iron lines, as well as of thermal X-ray spectra from accreting black
holes will lead in the near future to an experimental test of the no-hair
theorem.

本篇论文探讨了通过电磁波观测黑洞，从而实验证实哈斯 - 诺特定理的可能性，研究表明黑洞的四极矩对于哈斯 - 诺特定理的验证具有重要意义，从黑洞成像、热辐射等多方面都可得到高精度的观测值。