Curvature blow-up rates in spherically symmetric gravitational collapse to a Schwarzschild black hole

TL;DR

This paper investigates the precise rates at which curvature invariants blow up inside spherically symmetric black holes formed from gravitational collapse, revealing a new PDE-driven blow-up phenomenon influenced by scalar field behavior.

Contribution

It identifies a novel PDE mechanism affecting curvature blow-up rates in gravitational collapse, extending understanding beyond classical Schwarzschild models.

Findings

Kretschmann scalar blows up faster than in Schwarzschild due to mass inflation.

Blow-up rates vary and approach Schwarzschild rates at late times.

Scalar field behavior influences the curvature blow-up rates.

Abstract

We study the black hole interiors of spacetimes arising from gravitational collapse in the spherically symmetric Einstein-scalar field setting, and we investigate the precise blow-up rates of curvature and mass at the spacelike singularity near timelike infinity. We show in particular that the Kretschmann scalar blows up faster than in the Schwarzschild setting, due to mass inflation. Moreover, the blow-up rate is not constant and converges to the Schwarzschild rate towards timelike infinity and it depends on the precise late-time polynomial behaviour of the scalar field along the event horizon. This indicates a new blow-up phenomenon, driven by a PDE mechanism, rather than an ODE mechanism.