Non-linear instability of Kerr-type Cauchy horizons

TL;DR

This paper investigates the non-linear instability of Cauchy horizons inside realistic black holes, showing that diverging gravitational energy flux leads to singularities, with spacetime becoming asymptotically Petrov type N.

Contribution

It applies Hayward's general solution to analyze the non-linear instability of Kerr-type Cauchy horizons under minimal assumptions.

Findings

Diverging gravitational energy flux causes singularity formation.

Spacetime becomes asymptotically Petrov type N near the Cauchy horizon.

Results extend spherical case insights to more realistic black hole models.

Abstract

Using the general solution to the Einstein equations on intersecting null surfaces developed by Hayward, we investigate the non-linear instability of the Cauchy horizon inside a realistic black hole. Making a minimal assumption about the free gravitational data allows us to solve the field equations along a null surface crossing the Cauchy Horizon. As in the spherical case, the results indicate that a diverging influx of gravitational energy, in concert with an outflux across the CH, is responsible for the singularity. The spacetime is asymptotically Petrov type N, the same algebraic type as a gravitational shock wave. Implications for the continuation of spacetime through the singularity are briefly discussed.