The physics of the relativistic counter-streaming instability that drives mass inflation inside black holes

TL;DR

This paper explains the physical mechanism behind mass inflation inside black holes, showing how relativistic counter-streaming leads to exponential growth and eventual singularity, with implications for black hole interiors and quantum gravity.

Contribution

It provides a clear physical exposition and simple approximations for the mass inflation process, confirming their accuracy against nonlinear models and exploring its dependence on accretion and fluid properties.

Findings

Inflation accelerates more rapidly with lower accretion rates.

Inflation occurs only if the sound speed equals the speed of light in single-fluid models.

The end state of inflation is a spacelike singularity, not a null one.

Abstract

If you fall into a real astronomical black hole (choosing a supermassive black hole, to make sure that the tidal forces don't get you first), then you will probably meet your fate not at a central singularity, but rather in the exponentially growing, relativistic counter-streaming instability at the inner horizon first pointed out by Poisson & Israel (1990), who called it mass inflation. The chief purpose of this paper is to present a clear exposition of the physical cause and consequence of inflation in spherical, charged black holes. Inflation acts like a particle accelerator in that it accelerates cold ingoing and outgoing streams through each other to prodigiously high energies. Inflation feeds on itself: the acceleration is powered by the gravity produced by the streaming energy. The paper: (1) uses physical arguments to develop simple approximations that follow the evolution of inflation from ignition, through inflation itself, to collapse; (2) confirms that the simple approximations capture accurately the results of fully nonlinear one- and two-fluid self-similar models; (3) demonstrates that, counter-intuitively, the smaller the accretion rate, the more rapidly inflation exponentiates; (4) shows that in single perfect-fluid models, inflation occurs only if the sound speed equals the speed of light, supporting the physical idea that inflation in single fluids is driven by relativistic counter-streaming of waves; (5) shows that what happens during inflation up to the Planck curvature depends not on the distant past or future, but rather on events happening only a few hundred black hole crossing times into the past or future; (6) shows that, if quantum gravity does not intervene, then the generic end result of inflation is not a general relativistic null singularity, but rather a spacelike singularity at zero radius.