Mass inflation inside black holes revisited

• Published in: Classical and quantum gravity 2014-03, Vol.31 (5), p.55009
• Main Author: Dokuchaev, Vyacheslav I
• Format: Article
• Language: English
• Subjects: Approximation; black holes; Black holes (astronomy); Fluxes; general relativity; Horizon; Inflation; Mathematical analysis; Perturbation methods; Quantum gravity; singularities
• ISSN: 0264-9381; 1361-6382
• DOI: 10.1088/0264-9381/31/5/055009

The mass inflation phenomenon implies that black hole interiors are unstable due to a back-reaction divergence of the perturbed black hole mass function at the Cauchy horizon. The mass inflation was initially derived by using the generalized Dray-'t Hooft-Redmount (DTR) relation in the linear approximation of the Einstein equations near the perturbed Cauchy horizon of the Reissner-Nordström black hole. However, this linear approximation for the DTR relation is improper for the highly nonlinear behavior of back-reaction perturbations at the black hole horizons. An additional weak point in the standard mass inflation calculations is in a fallacious using of the global Cauchy horizon as a place for the maximal growth of the back-reaction perturbations instead of the local inner apparent horizon. It is derived the new spherically symmetric back-reaction solution for two counter-streaming light-like fluxes near the inner apparent horizon of the charged black hole by taking into account its separation from the Cauchy horizon. In this solution the back-reaction perturbations of the background metric are truly the largest at the inner apparent horizon, but, nevertheless, remain small. The back reaction, additionally, removes the infinite blue-shift singularity at the inner apparent horizon and at the Cauchy horizon.