Can falling of an electron into a black be treated as a process in which energy, charge, spin (angular momentum) and lepton number of the system are conserved?
Imagine a small volume of space that at $t_0$ contained no particles. Then N neutrons enter those volume of space. If N is sufficiently large they can form a black hole ($bh_0$). After its formation, $bh_0$ can absorb a proton and an electron with formation of a bit more massive neutral black hole $bh_1$ $$N n \longrightarrow bh_0 \\ bh_0+ p^+ + e^- \longrightarrow bh_1 $$
The black hole will emit Hawking-radiation and, therefore, will evaporate after sufficiently long time with formation of photons (and possibly a small number of other particles). So, for distant observer, $bh_1$ can be treated as an intermediate state of neutrons, proton and electron converting into photons.
$$N n + p^+ + e^- \longrightarrow (IntermediateState) \longrightarrow M \gamma$$
This process violates lepton number conservation.
The question is what is the best explanation of this thought experiment:
- lepton number is not conserved in interactions including gravitation forces, so there is a tiny probability of proton-electron interaction with formation of photon(s).
- black holes ara characterized not only by mass, charge, and angular momentum(spin), but also by leptonic number that affects which particles are formed upon black hole evaporation (contradicts "The no-hair theorem")
- falling of an electron into black hole should be accomplished by emission of a neutrino $$e^- + bh_0 \longrightarrow bh_1 + \nu_e, $$ where $bh_0$ and $bh_1$ are black hole before and after electron absorption.
