We show that the high-energy emission of GRBs originates in the inner engine : a Kerr black hole ( BH ) surrounded by matter and a magnetic field B _ { 0 } .
It radiates a sequence of discrete events of particle acceleration , each of energy { \cal E } = \hbar \Omega _ { eff } , the blackholic quantum , where \Omega _ { eff } = 4 ( m _ { Pl } / m _ { n } ) ^ { 8 } ( c a / G M ) ( B _ { 0 } ^ { 2 } / \rho _ { Pl } ) % \Omega _ { + } .
Here M , a = J / M , \Omega _ { + } = c ^ { 2 } \partial M / \partial J = ( c ^ { 2 } / G ) a / ( 2 Mr _ { + } ) and r _ { + } are the BH mass , angular momentum per unit mass , angular velocity and horizon ; m _ { n } is the neutron mass , m _ { Pl } , \lambda _ { Pl } = \hbar / ( m _ { Pl } c ) and \rho _ { Pl } = m _ { Pl } c ^ { 2 } / \lambda _ { Pl } ^ { 3 } , are the Planck mass , length and energy density .
Here and in the following use CGS-Gaussian units .
The timescale of each process is \tau _ { el } \sim \Omega _ { + } ^ { -1 } , along the rotation axis , while it is much shorter off-axis owing to energy losses such as synchrotron radiation .
We show an analogy with the Zeeman and Stark effects , properly scaled from microphysics to macrophysics , that allows us to define the BH magneton , \mu _ { BH } = ( m _ { Pl } / m _ { n } ) ^ { 4 } ( c a / G M ) e \hbar / ( Mc ) .
We give quantitative estimates for GRB 130427A adopting M = 2.3 ~ { } M _ { \odot } , c a / ( G M ) = 0.47 and B _ { 0 } = 3.5 \times 10 ^ { 10 } G. Each emitted quantum , { \cal E } \sim 10 ^ { 37 } erg , extracts only 10 ^ { -16 } times the BH rotational energy , guaranteeing that the process can be repeated for thousands of years .
The inner engine can also work in AGN as we here exemplified for the supermassive BH at the center of M87 .