Formation of extremal Reissner-Nordstr\"om black holes: insights from numerics

TL;DR

This paper numerically investigates the formation of extremal Reissner-Nordström black holes through gravitational collapse, analyzing how different scalar field configurations influence the minimum mass needed for black hole formation.

Contribution

It provides a numerical analysis of the characteristic gluing method for various scalar field Ans"atze, revealing how the minimum mass for black hole formation depends on the field configuration and parameters.

Findings

Gluing is possible only if the final black hole mass exceeds a certain threshold.

The minimum mass varies significantly with different scalar field Ans"atze.

Including a scalar field mass or cosmological constant affects the maximum mass-to-charge ratio for gluing.

Abstract

An extremal Reissner-Nordstr\"om black hole can form in finite time in the gravitational collapse of a massless charged scalar field. The proof of this is based on the method of characteristic gluing, which involves making an Ansatz for the scalar field at the horizon. We perform a numerical investigation of the characteristic gluing procedure for several different Ans\"atze. In each case, gluing is possible only if the final black hole mass is large enough. We find that the minimum required mass varies significantly for different Ans\"atze. We also consider the effect of including a mass term for the scalar field. In this case, for each Ansatz we determine the maximum mass-to-charge ratio for the scalar field such that gluing is possible. Analogous results are obtained for a non-zero cosmological constant.