Towards a general description of the interior structure of rotating black holes

TL;DR

This paper proposes a theoretical framework for understanding the interior structure of slowly accreting rotating black holes, emphasizing mass inflation, shear-free spacetime, and the role of gravitational waves and particle collisions in the inflation process.

Contribution

It introduces a shear-free approximation and a specific line-element model for rotating black hole interiors, extending previous inflation theories with new analytical insights.

Findings

Outgoing and ingoing particles focus along null directions near the inner horizon.

A shear-free set of equations for black hole interiors is derived.

Super-Planckian collisions trigger entropy production, ending inflation.

Abstract

The purpose of this paper is to present a number of proposals about the interior structure of a rotating black hole that is accreting slowly, but in an arbitrary time- and space-dependent fashion. The proposals could potentially be tested with numerical simulations. Outgoing and ingoing particles free-falling in the parent Kerr geometry become highly focused along the principal outgoing and ingoing null directions as they approach the inner horizon, triggering the mass inflation instability. The original arguments of Barrabes, Israel & Poisson (1990) regarding inflation in rotating black holes are reviewed, and shown to be based on Raychauduri's equation applied along the outgoing and ingoing null directions. It is argued that gravitational waves should behave in the geometric optics limit, and consequently that the spacetime should be almost shear-free. A full set of shear-free equations is derived. A specific line-element is proposed, which is argued should provide a satisfactory approximation during early inflation. Finally, it is argued that super-Planckian collisions between outgoing and ingoing particles will lead to entropy production, bringing inflation to an end, and precipitating collapse.