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We review the physical origins for possible visible images of the supermassive black hole M87* in the galaxy M87 and SgrA* in the Milky Way Galaxy. The classical dark black hole shadow of the maximal size is visible in the case of luminous background behind the black hole at the distance exceeding the so-called photon spheres. The notably smaller dark shadow (dark silhouette) of the black hole event horizon is visible if the black hole is highlighted by the inner parts of the luminous accreting matter inside the photon spheres. The first image of the supermassive black hole M87 *, obtained by the Event Horizon Telescope collaboration, shows the lensed dark image of the southern hemisphere of the black hole event horizon globe, highlighted by accreting matter, while the classical black hole shadow is invisible at all. A size of the dark spot on the Event Horizon Telescope (EHT) image agrees with a corresponding size of the dark event horizon silhouette in a thin accretion disk model in the case of either the high or moderate value of the black hole spin, $a\gtrsim0.75$., Comment: Published version, 21 pages, 12 figures

We argue that a genuine image of the black hole viewed by a distant observer is not its shadow, but a more compact event horizon image probed by the luminous matter plunging into black hole. The external border of the black hole shadow is washed out by radiation from matter plunging into black hole and approaching the event horizon. This effect will crucially influence the results of future observations by the Event Horizon Telescope. We show that gravitational lensing of the luminous matter plunging into black hole provides the possibility for visualization of the event horizon. The lensed image of the event horizon is formed by the highly red-shifted photons emitted by the plunging matter very near the black hole event horizon and detected by a distant observer. The resulting event horizon image is a gravitationally lensed projection on the celestial sphere of the whole black hole event horizon sphere. Seemingly, black holes are the unique objects in the Universe which may be viewed by distant observers at once from both the front and back sides., Comment: 7 pages, 9 figures, new references added

The gravitational lensing of a finite star moving around a rotating Kerr black hole has been numerically calculated. Calculations for the direct image of the star and for the first and second light echoes have been performed for the star moving with an orbital period of 3.22 h around the supermassive black hole SgrA* at the Galactic Center. Time dependences for the observed star position on the celestial sphere, radiation flux from the star, frequency of detected radiation, major and minor semiaxes of the lensed star image have been calculated and plotted. The detailed observation of such lensing requires a space interferometer such as the Russian Millimetron project., Comment: 8 pages, 12 figures. Related video is available at https://youtu.be/P6DneV0vk7U

Primordial black holes (PBH) could account for variety of phenomena like dark matter, reionization of the Universe, early quasars, coalescence of black holes registered through gravitational waves recently. Each phenomenon relates to PBH of a specific mass range. PBH mass spectra varies in a wide range depending on specific model. Earlier we have shown that PBH with monochromatic mass distribution around $5\times 10^{16}$ g value allow to re-ionize the Universe moderately. Here we show that reionization effect and contribution to dark matter can be simultaneously enhanced with more natural extended mass distribution in the range around the same mass value., Comment: 6 pages, 6 figures. Accepted for publication in International Journal of Modern Physics D