13 citations · 49 across the 13 of their papers we have counts for
15 papers
The linear instability of Kasner spacetimes
Oliver Petersen
We prove linear stability of Kasner spacetimes in the direction of the Big Bang, up to an explicit finite dimensional space of non-decaying self-similar solutions. The fastest grow…
Dual modes in Kerr spacetimes and the Whiting transform: Mode stability revisited
Oliver Petersen, András Vasy
The purpose of the paper is to place Whiting's classical growing mode stability argument, extended to real frequencies by Shlapentokh-Rothman for the scalar wave equation and by An…
Conditional non-linear stability of Kerr-de Sitter spacetimes in the full subextremal range
Peter Hintz, Oliver Petersen, András Vasy
We show the stability of Kerr-de Sitter black holes, in the full subextremal range, as solutions of the vacuum Einstein equation with a positive cosmological constant under the ass…
Formation of quiescent big bang singularities
Hans Oude Groeniger, Oliver Petersen, Hans Ringström
Hawking's singularity theorem says that cosmological solutions arising from initial data with positive mean curvature have a past singularity. However, the nature of the singularit…
Stationarity and Fredholm Theory in Subextremal Kerr-de Sitter Spacetimes
Oliver Petersen, András Vasy
In a recent paper, we proved that solutions to linear wave equations in a subextremal Kerr-de Sitter spacetime have asymptotic expansions in quasinormal modes up to a decay order g…
Wave equations in the Kerr-de Sitter spacetime: the full subextremal range
Oliver Petersen, András Vasy
We prove that solutions to linear wave equations in a subextremal Kerr-de Sitter spacetime have asymptotic expansions in quasinormal modes up to a decay order given by the normally…
The asymptotic expansion of the spacetime metric at the event horizon
Klaus Kroencke, Oliver Petersen
Hawking's local rigidity theorem, proven in the smooth setting by Alexakis-Ionescu-Klainerman, says that the event horizon of any stationary non-extremal black hole is a non-degene…
Analyticity of quasinormal modes in the Kerr and Kerr-de Sitter spacetimes
Oliver Petersen, András Vasy
We prove that quasinormal modes (or resonant states) for linear wave equations in the subextremal Kerr and Kerr-de Sitter spacetimes are real analytic. The main novelty of this pap…
Convergence of the Ricci flow to Ricci-flat ALE manifolds and positive scalar curvature rigidity
Klaus Kroencke, Oliver Lindblad Petersen
We prove stability of integrable ALE manifolds with a parallel spinor under Ricci flow, given an initial metric which is close in , for any , where…
Long-time estimates for heat flows on ALE manifolds
Klaus Kroencke, Oliver Lindblad Petersen
We consider the heat equation associated to Schrödinger operators acting on vector bundles on asymptotically locally Euclidean (ALE) manifolds. Novel decay estimates ar…
Extension of Killing vector fields beyond compact Cauchy horizons
Oliver Lindblad Petersen
We prove that any compact Cauchy horizon with constant non-zero surface gravity in a smooth vacuum spacetime is a smooth Killing horizon. The novelty here is that the Killing vecto…
Symmetries of vacuum spacetimes with a compact Cauchy horizon of constant non-zero surface gravity
Oliver Petersen, István Rácz
We prove that any smooth vacuum spacetime containing a compact Cauchy horizon with surface gravity that can be normalised to a non-zero constant admits a Killing vector field. This…
On the Cauchy problem for the linearised Einstein equation
Oliver Lindblad Petersen
A classical problem in general relativity is the Cauchy problem for the linearised Einstein equation (the initial value problem for gravitational waves) on a globally hyperbolic va…
Wave equations with initial data on compact Cauchy horizons
Oliver Lindblad Petersen
We study the following problem: Given initial data on a compact Cauchy horizon, does there exist a unique solution to wave equations on the globally hyperbolic region? Our main res…
The mode solution of the wave equation in Kasner spacetimes and redshift
Oliver Lindblad Petersen
We study the mode solution to the Cauchy problem of the scalar wave equation in Kasner spacetimes. As a first result, we give the explicit mode solution in axisymmetric…