Curvature blow-up rates in spherically symmetric gravitational collapse to a Schwarzschild black hole
arXiv:2004.11831
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.
arXiv comment45 pages
References in corpus (15)
- Quasinormal modes and Strong Cosmic Censorship
- A proof of Price's law for the collapse of a self-gravitating scalar field
- The global non-linear stability of the Kerr-de Sitter family of black holes
- Black holes without spacelike singularities
- Strong cosmic censorship in de Sitter space
- Proof of linear instability of the Reissner-Nordström Cauchy horizon under scalar perturbations
- Time-Translation Invariance of Scattering Maps and Blue-Shift Instabilities on Kerr Black Hole Spacetimes
- Linear waves in the interior of extremal black holes I
- Boundedness and decay of scalar waves at the Cauchy horizon of the Kerr spacetime
- Boundedness of massless scalar waves on Kerr interior backgrounds
- On the backward stability of the Schwarzschild black hole singularity
- Asymptotics for scalar perturbations from a neighborhood of the bifurcation sphere
- Stable space-like singularity formation for axi-symmetric and polarized near-Schwarzschild black hole interiors
- Numerical evolution of the interior geometry of charged black holes
- Linear systems of wave equations on cosmological backgrounds with convergent asymptotics