  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 ${\cal E} = \hbar\,\Omega_{\rm eff}$, the \textit{blackholic
quantum}, where $\Omega_{\rm eff} =4(m_{\rm
Pl}/m_n)^8(c\,a/G\,M)(B_0^2/\rho_{\rm Pl})\Omega_+$. Here $M$, $a=J/M$,
$\Omega_+=c^2\partial M/\partial J=(c^2/G)\,a/(2 M r_+)$ and $r_+$ are the BH
mass, angular momentum per unit mass, angular velocity and horizon; $m_n$ is
the neutron mass, $m_{\rm Pl}$, $\lambda_{\rm Pl}=\hbar/(m_{\rm Pl}c)$ and
$\rho_{\rm Pl}=m_{\rm Pl}c^2/\lambda_{\rm Pl}^3$, are the Planck mass, length
and energy density. {Here and in the following use CGS-Gaussian units}. The
time\-scale of each process is $\tau_{\rm el}\sim \Omega_+^{-1}$, {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", $\mu_{\rm BH}=(m_{\rm Pl}/m_n)^4(c\,a/G\,M)e\,\hbar/(M c)$. 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.
