The blackholic quantum

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 $${{\mathscr {E}}} = \hbar \,\varOmega _{\mathrm{eff}}$$, the blackholic quantum, where $$\varOmega _{\mathrm{eff}} =4(m_{\mathrm{Pl}}/m_n)^8(c\,a/G\,M)(B_0^2/\rho _\mathrm{Pl})\varOmega _+$$. Here M, $$a=J/M$$, $$\varOmega _+=c^2\partial M/\partial J=(c^2/G)\,a/(2 M r_+)$$ and $$r_+$$ are the BH mass, angular momentum per unit mass, angular velocity and horizon; $$m_n$$ is the neutron mass, $$m_{\mathrm{Pl}}$$, $$\lambda _{\mathrm{Pl}}=\hbar /(m_{\mathrm{Pl}}c)$$ and $$\rho _{\mathrm{Pl}}=m_{\mathrm{Pl}}c^2/\lambda _{\mathrm{Pl}}^3$$, are the Planck mass, length and energy density. Here and in the following use CGS-Gaussian units. The timescale of each process is $$\tau _{\mathrm{el}}\sim \varOmega _+^{-1}$$, 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, $$\mu _{\mathrm{BH}}=(m_{\mathrm{Pl}}/m_n)^4(c\,a/G\,M)e\,\hbar /(M c)$$. 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, $$\mathcal{E}\sim 10^{37}$$ 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.