Collapsing and static thin massive charged dust shells in a Reissner-Nordstr\"om black hole background in higher dimensions

TL;DR

This paper investigates the dynamics of charged thin shells collapsing into or static around higher-dimensional Reissner-Nordström black holes, deriving equations of motion, analyzing stability, and exploring implications for cosmic censorship and black hole formation.

Contribution

It provides the first derivation of shell equations of motion in higher dimensions and proves constraints on extremal shells, extending previous four-dimensional results to higher-dimensional spacetimes.

Findings

Extremal shells with mass equal to charge can only stay in neutral equilibrium outside the horizon.

Oscillatory shells always enter the horizon and reemerge in a new asymptotic region.

Stable equilibrium positions are possible for overcharged shells with no horizons.

Abstract

The problem of a spherically symmetric charged thin shell of dust collapsing gravitationally into a charged Reissner-Nordstr\"om black hole in $d$ spacetime dimensions is studied within the theory of general relativity. Static charged shells in such a background are also analyzed. First a derivation of the equation of motion of such a shell in a $d$-dimensional spacetime is given. Then a proof of the cosmic censorship conjecture in a charged collapsing framework is presented, and a useful constraint which leads to an upper bound for the rest mass of a charged shell with an empty interior is derived. It is also proved that a shell with total mass equal to charge, i.e., an extremal shell, in an empty interior, can only stay in neutral equilibrium outside its gravitational radius. This implies that it is not possible to generate a regular extremal black hole by placing an extremal dust thin shell within its own gravitational radius. Moreover, it is shown, for an empty interior, that the rest mass of the shell is limited from above. Then several types of behavior of oscillatory charged shells are studied. In the presence of a horizon, it is shown that an oscillatory shell always enters the horizon and reemerges in a new asymptotically flat region of the extended Reissner-Nordstr\"om spacetime. On the other hand, for an overcharged interior, i.e., a shell with no horizons, an example showing that the shell can achieve a stable equilibrium position is presented. The results presented have applications in brane scenarios with extra large dimensions, where the creation of tiny higher dimensional charged black holes in current particle accelerators might be a real possibility, and generalize to higher dimensions previous calculations on the dynamics of charged shells in four dimensions.