The blackholic quantum (1907.08066v3)

Abstract: 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.