Abstract We report on astrophysical aspects of fully innovative very wide-field X-ray telescopes with high sensitivity. The prototypes are very promising, allowing the proposals for space projects with very wide-field Lobster-eye X-ray optics to be considered. The novel telescopes will monitor the sky with unprecedented sensitivity and angular resolution of order of 1 arcmin. They are expected to contribute essentially to study of various astrophysical objects such as AGN, SNe, Gamma-ray bursts (GRBs), X-ray flashes (XRFs), galactic binary sources, stars, CVs, X-ray novae, various transient sources, etc.
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