Challenging the weak cosmic censorship conjecture with charged quantum particles

Abstract

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-Nordström black hole by the quantum tunneling of charged particles. We consider the scattering of spin-0 and spin-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-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-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.

Test of the weak cosmic censorship conjecture with a charged scalar field and dyonic Kerr–Newman black holes

“…is obtained from (37). The right hand side in (38) is the same as the left hand side in (25), and in the extremal case it is M 2(M 2 +a 2 ) dη.…”

Quasinormal modes of extremal black holes

“…Furthermore, the study of spin-0 and spin-1/2 electrically charged, massless fields around a RN black hole can be simplified if the same ansatz used for Kerr perturbations is employed. Indeed, by doing so, one can show that the Klein-Gordon and the Dirac equations, in the RN metric, can be separated and recast as new equations which are analogous to the Teukolsky equations [19,20]. The angular equation assumes the form (2.2) with aω = 0, while the radial one assumes the form (2.3) with K = ωr 2 −qQr and X = 4isωr−2isqQ−λ (q denotes the charge of the field).…”

Superradiance on the Reissner–Nordstrøm metric

“…It would also be interesting to check the agreement of our numerical experiments with the low frequency regime (M ω << 1) calculation of the transmission coefficient in [23]. This would require to take larger and larger values of the mass M of the black hole and to check that the transmission coefficient tends to −1, or equivalently that the gain tends to 2.…”