Challenging the weak cosmic censorship conjecture with charged quantum particles

Motivated by the recent attempts to violate the weak cosmic censorship conjecture for near-extreme black holes, we consider the possibility of overcharging a near-extreme Reissner-Nordstr\"om black hole by the quantum tunneling of charged particles. We consider the scattering of spin-0 and spin-$\frac{1}{2}$ particles by the black hole in a unified framework and obtain analytically, for the first time, the pertinent reflection and transmission coefficients without any small charge approximation. Based on these results, we propose some gedanken experiments that could lead to the violation of the weak cosmic censorship conjecture due to the (classically forbidden) absorption of small energy charged particles by the black hole. As for the case of scattering in Kerr spacetimes, our results demonstrate explicitly that scalar fields are subject to (electrical) superradiance phenomenon, while spin-$\frac{1}{2}$ fields are not. Superradiance impose some limitations on the gedanken experiments involving spin-0 fields, favoring, in this way, the mechanisms for creation of a naked singularity by the quantum tunneling of spin-$\frac{1}{2}$ charged fermions. We also discuss the implications that vacuum polarization effects and quantum statistics might have on these gedanken experiments. In particular, we show that they are not enough to prevent the absorption of incident small energy particles and, consequently, the formation of a naked singularity.

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