arXiv subjects

Stefanos Aretakis

Publications and source records attributed to Stefanos Aretakis.

25 records · Page 2Linked to original sources

arXiv2013

A note on instabilities of extremal black holes under scalar perturbations from afar

In previous work of the author it was shown that instabilities of solutions to the wave equation develop asymptotically along the event horizon of extremal Kerr provided a certain expression H of the initial data is non-trivial on the horizon. In this note we remove this restriction by showing that instabilities develop even from initial data supported arbitrarily far away from the horizon (for which, in particular, H=0). The latter instabilities concern one order higher derivatives compared to the case where H is non-zero. The result also applies to extremal Reissner-Nordstrom. This note was motivated by numerical analysis of Lucietti, Murata, Reall and Tanahashi.

gr-qc↗

arXiv2013

Nonlinear instability of scalar fields on extremal black holes

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.

gr-qc↗

arXiv2013

Horizon Instability of Extremal Black Holes

We show that axisymmetric extremal horizons are unstable under linear scalar perturbations. Specifically, we show that translation invariant derivatives of generic solutions to the wave equation do not decay along such horizons as advanced time tends to infinity, and in fact, higher order derivatives blow up. This result holds in particular for extremal Kerr-Newman and Majumdar-Papapetrou spacetimes and is in stark contrast with the subextremal case for which decay is known for all derivatives along the event horizon.

gr-qc↗

arXiv2011

The Wave Equation on Extreme Reissner-Nordström Black Hole Spacetimes: Stability and Instability Results

We consider solutions to the linear wave equation on a suitable globally hyperbolic subset of an extreme Reissner-Nordstrom spacetime, arising from regular initial data prescribed on a Cauchy hypersurface crossing the future event horizon. We obtain boundedness, decay, non-decay and blow-up results. Our estimates hold up to and including the event horizon. The fundamental new aspect of this problem is the degeneracy of the redshift on the event horizon. Several new analytical features of degenerate horizons are also presented.

math.AP↗

arXiv2011

Decay of Axisymmetric Solutions of the Wave Equation on Extreme Kerr Backgrounds

We study the Cauchy problem for the wave equation on extreme Kerr backgrounds under axisymmetry. Specifically, we consider regular axisymmetric initial data prescribed on a Cauchy hypersurface S which connects the future event horizon with spacelike or null infinity, and we solve the linear wave equation on the domain of dependence of S. We show that the spacetime integral of an energy-type density is bounded by the initial conserved flux corresponding to the stationary Killing field T, and we derive boundedness of the non-degenerate energy flux corresponding to a globally timelike vector field N. Finally, we prove uniform pointwise boundedness and power-law decay for solutions to the wave equation. Our estimates hold up to and including the event horizon. We remark that these results do not yield decay for the derivatives transversal to the horizon, and this is suggestive that these derivatives may satisfy instability properties analogous to those shown in our previous work on extreme Reissner-Nordstrom backgrounds.

gr-qc↗

arXiv2011

Stability and Instability of Extreme Reissner-Nordström Black Hole Spacetimes for Linear Scalar Perturbations II

This paper contains the second part of a two-part series on the stability and instability of extreme Reissner-Nordstrom spacetimes for linear scalar perturbations. We continue our study of solutions to the linear wave equation on a suitable globally hyperbolic subset of such a spacetime, arising from regular initial data prescribed on a Cauchy hypersurface crossing the future event horizon. We here obtain definitive energy and pointwise decay, non-decay and blow-up results. Our estimates hold up to and including the horizon. A hierarchy of conservations laws on degenerate horizons is also derived.

gr-qc↗

arXiv2011

Stability and Instability of Extreme Reissner-Nordström Black Hole Spacetimes for Linear Scalar Perturbations I

We study the problem of stability and instability of extreme Reissner-Nordstrom spacetimes for linear scalar perturbations. Specifically, we consider solutions to the linear wave equation on a suitable globally hyperbolic subset of such a spacetime, arising from regular initial data prescribed on a Cauchy hypersurface crossing the future event horizon. We obtain boundedness, decay and non-decay results. Our estimates hold up to and including the horizon. The fundamental new aspect of this problem is the degeneracy of the redshift on the event horizon. Several new analytical features of degenerate horizons are also presented.

gr-qc↗