The observed properties of Gamma-Ray Bursts such as rapid variability of\nX-ray light curve and large energies strongly signature the compact binary,\ndisk accreting system. Our work particularly highlights the extremely rotating,\ndisk accreting black holes as physical source of the flares variability and\nX-ray afterglow plateaus of GRBs. We investigate the compact binary mergers\n(neutron star - neutron star and neutron star onto black hole) and gravitational\ncore collapse of super massive star, where in both cases hyper-accreting\nKerr hole is formed. The core collapse in a powerful gravitational wave explained\nas a potential source for the radiated flux of hard X-rays spectrum.\nWe described the evolution of rapidly rotating, accreting BH in general relativity\nand the relativistic accretion flow in resistive MHD for viscous radiation.\nWe compute the structure of accretion disk, the accretion luminosity of\nthe dynamical evolution of inner accretion disk and precisely determine their\nradiation spectra, and compare to observational data of X-ray satellites. Finally,\nwe obtained the resulting disk radiation basically explained as the X-ray\nluminosity of the central source, such as LMC X-1 and GRO J1655-40. These\nresults are interestingly consistent with observational data of galactic X-ray\nsource binary systems such as X-ray luminosities of Cygnus X-1 and Seyfert\ngalaxies (NGC 3783, NGC 4151, NGC 4486 (Messier 87)) which are powerful\nemitters in X-ray and gamma-ray wavebands of the observed X-ray variability\nwith typical luminosity.
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