High Resolution Imaging of a Black Hole Shadow with Millimetron Orbit
  around Lagrange Point L2
  Imaging of the shadow around supermassive black hole (SMBH) horizon with a
very long baseline interferometry (VLBI) is recognized recently as a powerful
tool for experimental testing of Einstein's General relativity. The Event
Horizon Telescope (EHT) has demonstrated that an Earth-extended VLBI with the
maximum long base ($D=10,700$ km) can provide a sufficient angular resolution
$\theta\sim 20~\mu$as at $\lambda=1.3$ mm ($\nu=230$ GHz) for imaging the
shadow around SMBH located in the galaxy M87$^\ast$. However, the accuracy of
critically important characteristics, such as the asymmetry of the
crescent-shaped bright structure around the shadow and the sharpness of a
transition zone between the shadow floor and the bright crescent silhouette,
both of order $\Delta\theta\sim 4~\mu$as, is still to be improved. In our
previous paper we have shown that Space-Earth VLBI observation within a joint
Millimetron and EHT configuration at the near-Earth high elliptical orbit (HEO)
can considerably improve the image quality. Even more solid grounds for firm
experimental validation of General relativity can be obtained with a higher
resolution available within the joint Millimetron and EHT program at the
Lagrangian point L2 in the Sun-Earth system with an expected imaging resolution
at 230~GHz of $\Delta\theta\sim 5~\mu$as. In this paper we argue that in spite
of limitations of L2 orbit, an adequate sparse $(u,v)$ coverage can be achieved
and the imaging of the shadows around Sgr A$^\ast$ and M87$^\ast$ can be
performed with a reasonable quality.
