Mass Inflation in Dynamical Gravitational Collapse of a Charged Scalar Field

Abstract

During the last ten years evidence has been mounting that generically the Cauchy horizon inside a charged or a spinning black hole becomes a null, weak singularity which is a precursor of a strong, spacelike singularity along the r 0 hypersurface. We present here the missing link in this picture: A complete calculation from a regular initial data to the formation of a black hole and its inner singularities. We follow the gravitational collapse of a self-gravitating charged massless scalar field and observe the formation of an apparent horizon, a null, weak, mass-inflation singularity along the Cauchy horizon, and a final, spacelike, central singularity. [S0031-9007(98)06951-8] PACS numbers: 04.70.Bw, 04.25.Dm, 04.40.NrThe no-hair conjecture, introduced by Wheeler [1] in the early 1970s, states that the external field of a black-hole relaxes to a Kerr-Newman field characterized solely by the black-hole's mass, charge and angular-momentum. This simple picture describing the exterior of a black hole is in dramatic contrast with its interior. The singularity theorems of Penrose and Hawking [2] predict the occurrence of inevitable spacetime singularities as a result of a gravitational collapse in which a black hole forms. According to the weak cosmic censorship conjecture [3] these spacetime singularities are hidden beneath the black hole's event horizon. However, these theorems tell us nothing about the nature of these spacetime singularities. In particular, the final outcome of a generic gravitational collapse is still an open question in general relativity.Until recently, our physical intuition regarding the nature of these inner singularities was largely based on the known static or stationary black-hole solutions: Schwarzschild (spacelike, strong, and unavoidable central singularity), Reissner-Nordström and Kerr (timelike, strong singularity). Further insight was gained from the work of Belinsky, Khalatnikov, and Lifshitz [4] who found a strong oscillatory spacelike singularity. However, a new and drastically different picture of these inner black-hole singularities has emerged in the last few years, according to which the Cauchy horizon (CH) inside charged or spinning black holes is transformed into a null, weak singularity [5][6][7][8][9]. The CH singularity is weak in the sense that an infalling observer which hits this null singularity experiences only a finite tidal deformation [7,8]. Nevertheless, curvature scalars (namely, the Newman-Penrose Weyl scalar C 2 ) diverge at the CH, a phenomena known as mass inflation [6]. The physical mechanism which underlies this CH singularity is actually quite simple: small perturbations, which are remnants of the gravitational collapse outside the collapsing object are gravitationally blueshifted as they propagate in the black hole's interior parallel to the CH [10] (the mass-inflation scenario itself includes in addition an outgoing radiation flux which irradiates the CH. This outgoing flux repre-sents a portion of the ingoing radiation which is scattered inside the blac...

Dilatons and the dynamical collapse of charged scalar field

“…Our results are consistent with those obtained in Refs. [25,28,30]. In what follows, the Penrose diagram of the latter spacetime shall be essential for our further analysis.…”

“…On the other hand, in [28,29] it was explicitly demonstrated the the mass inflation occurred during a dynamical charged gravitational collapse. Starting with the regular spacetime, the evolution through the formation of an apparent horizon, then the Cauchy horizon and a final singularity was performed.…”

Inside charged black holes. I. Baryons

“…Dimensional analysis of the spherically symmetric coupled Einstein-Maxwell equations (34) and (43), along with the definitions (21) of the acceleration g and (24) of the interior mass M , combined with the equation of state (39) of the baryonic fluid, the energy-momentum (41) of the electric field, and the phenomenological conductivity (48), reveals the following quantities to be dimensionless:…”

“…Analytic and numerical work on spherically symmetric collapse has commonly modeled the fluid accreted by the black hole as a massless scalar field, usually taken to be uncharged [7,9,11,12,13,14,15,24,27,32,33,38,50,56], but sometimes charged [26,46,48,49,61,71]. A key property of a massless scalar field is that it allows waves to counter-stream relativistically through each other, which allows the phenomenon of mass inflation on the Cauchy horizon to occur.…”

Semiclassical geometry of charged black holes

“…The physical relevance of much of the extended structure is questionable, however [3,4,5,6,7]. At the classical level, a dynamical instability, referred to as mass inflation, manifests itself when in-and outgoing energy fluxes cross near the inner horizon, replacing it by an initially null singularity which turns spacelike deep inside the black hole [8,9,10,11,12]. This null singularity is relatively weak, however, with finite integrated tidal effects acting on extended timelike observers [9], leaving open the possibility of extending the physical spacetime through it.…”