# Inflation followed by Belinskii-Khalatnikov-Lifshitz collapse inside accreting, rotating black holes

## TL;DR

This paper provides numerical evidence that mass inflation inside accreting, rotating black holes leads to a Belinskii-Khalatnikov-Lifshitz oscillatory collapse, resulting in a spacelike singularity, by simulating all gravitational degrees of freedom.

## Contribution

It is the first to numerically demonstrate the transition from mass inflation to BKL collapse inside rotating black holes using full gravitational dynamics.

## Key findings

- Mass inflation is followed by BKL oscillatory collapse.
- Collapse results in a spacelike singularity.
- Full gravitational degrees of freedom are involved in the simulation.

## Abstract

Numerical evidence is presented that the Poisson-Israel mass inflation instability at the inner horizon of an accreting, rotating black hole is generically followed by Belinskii-Khalatnikov-Lifshitz oscillatory collapse to a spacelike singularity. The computation involves following all 6 degrees of freedom of the gravitational field. To simplify the problem, the computation takes as initial conditions the conformally separable solutions of arXiv:1010.1269, arXiv:1010.1271 just above the inner horizon of a slowly accreting, rotating black hole, and integrates the equations inward along single latitudes.