Nonlinear instability of scalar fields on extremal black holes
General Relativity and Quantum Cosmology
2015-06-15 v1 High Energy Physics - Theory
Analysis of PDEs
Abstract
We prove a new type of finite time blow-up for a class of semilinear wave equations on extremal black holes. The initial data can be taken to be arbitrarily close to the trivial data. The first singularity occurs along the (degenerate) future event horizon. No analogue of this instability occurs for subextremal black holes or the Minkowski spacetime.
Keywords
Cite
@article{arxiv.1304.4616,
title = {Nonlinear instability of scalar fields on extremal black holes},
author = {Stefanos Aretakis},
journal= {arXiv preprint arXiv:1304.4616},
year = {2015}
}
Comments
6 pages, 2 figures, to appear in Phys. Rev. D