# The Meissner effect for weakly isolated horizons

## TL;DR

This paper proves that rapidly spinning black holes, even with accretion disks and strong magnetic fields, expel magnetic fields, demonstrating a gravitational analog of the Meissner effect known in superconductors.

## Contribution

It provides the first full general relativity proof that spinning black holes exhibit the Meissner effect, extending previous vacuum-based results to more realistic astrophysical scenarios.

## Key findings

- Rapidly spinning black holes expel magnetic fields.
- The Meissner effect applies even with accretion disks.
- Expulsion occurs for strong magnetic fields.

## Abstract

Black holes are important astrophysical objects describing an end state of stellar evolution, which are observed frequently. There are theoretical predictions that Kerr black holes with high spins expel magnetic fields. However, Kerr black holes are pure vacuum solutions, which do not include accretion disks, and additionally previous investigations are mainly limited to weak magnetic fields. We prove for the first time in full general relativity that generic rapidly spinning black holes including those deformed by accretion disks still expel even strong magnetic fields. Analogously to a similar property of superconductors, this is called Meissner effect.