# On neutralization of charged black holes

## TL;DR

This paper investigates how charged, spinning black holes (Kerr-Newman) tend to become neutralized by oppositely charged particles, using particle trajectory analysis without magnetospheres, and finds that neutralization is likely.

## Contribution

It provides the first detailed analysis of Kerr-Newman black hole neutralization without magnetospheres, revealing a universal probability dependence on particle charge.

## Key findings

- Oppositely charged particles have higher fall probability into the black hole.
- Charged, spinning black holes without magnetospheres are likely quickly neutralized.
- The neutralization process depends universally on the particle's charge.

## Abstract

For non-spinning, charged (Reissner-Nordstr\"om) black holes, the particles with an opposite sign of charge with respect to that of the black hole will be pulled into the black hole by the extra electromagnetic force. Such a hole will be quickly neutralized so that there should not exist significantly charged, non-spinning black holes in the universe. The case of spinning, charged (Kerr-Newmann) black holes is more complicated. For a given initial position and initial velocity of the particle, an oppositely charged particle does not always more easily fall into the black hole than a neutral particle. The possible existence of a magnetosphere further complicate the picture. One therefore cannot straightforwardly conclude that a charged spinning black hole will be neutralized. In this paper, we make the first step to investigate the neutralization of Kerr-Newmann black holes without introducing a magnetosphere. We track the particle trajectories under the influence of the curved spacetime and the electromagnetic field carried by the spinning, charged black hole. A statistical method is used to investigate the neutralization problem. We find a universal dependence of the falling probability into the black hole on the charge of the test particle, with the oppositely charged particles having a higher probability of falling. We therefore conclude that charged, spinning black holes without a magnetosphere should be quickly neutralized, consistent with people's intuition. The neutralization problem of Kerr-Newmann black holes with a co-rotating force-free magnetosphere is subject to further studies.