315 citations · 1.1k across the 35 of their papers we have counts for
38 papers
The linearized Einstein equations with sources
Peter Hintz
On vacuum spacetimes of general dimension, we study the linearized Einstein vacuum equations with a spatially compactly supported and (necessarily) divergence-free source. We prove…
Gluing small black holes along timelike geodesics I: formal solution
Peter Hintz
Given a smooth globally hyperbolic -dimensional spacetime satisfying the Einstein vacuum equations (possibly with cosmological constant) and an inextendible timelike geodesi…
Linear waves on asymptotically flat spacetimes. I
Peter Hintz
We introduce a novel framework for the analysis of linear wave equations on nonstationary asymptotically flat spacetimes, under the assumptions of mode stability and absence of zer…
Microlocal analysis near null infinity in asymptotically flat spacetimes
Peter Hintz, András Vasy
We present a novel approach to the analysis of regularity and decay for solutions of wave equations in a neighborhood of null infinity in asymptotically flat spacetimes of any dime…
Exterior stability of Minkowski space in generalized harmonic gauge
Peter Hintz
We give a short proof of the existence of a small piece of null infinity for -dimensional spacetimes evolving from asymptotically flat initial data as solutions of the Einst…
Microlocal analysis of operators with asymptotic translation- and dilation-invariances
Peter Hintz
On a suitable class of non-compact manifolds, we study (pseudo)differential operators which feature an asymptotic translation-invariance along one axis and an asymptotic dilation-i…
Underdetermined-elliptic PDE on asymptotically Euclidean manifolds, and generalizations
Peter Hintz
We study underdetermined-elliptic linear partial differential operators on asymptotically Euclidean manifolds, such as the divergence operator on 1-forms or symmetric 2-tensors…
Gluing small black holes into initial data sets
Peter Hintz
We prove a strong localized gluing result for the general relativistic constraint equations (with or without cosmological constant) in spatial dimensions. We glue an -…
Mode stability and shallow quasinormal modes of Kerr-de Sitter black holes away from extremality
Peter Hintz
A Kerr-de Sitter black hole is a solution of the Einstein vacuum equations with cosmological constant . It describes a black hole with ma…
Elliptic parametrices in the 0-calculus of Mazzeo and Melrose
Peter Hintz
The purpose of this note is to spell out the details of the construction of parametrices for fully elliptic uniformly degenerate pseudodifferential operators on manifolds with…
Quasinormal modes of small Schwarzschild-de Sitter black holes
Peter Hintz, YuQing Xie
We study the behavior of the quasinormal modes (QNMs) of massless and massive linear waves on Schwarzschild-de Sitter black holes as the black hole mass tends to 0. Via uniform est…
Quasinormal modes and dual resonant states on de Sitter space
Peter Hintz, YuQing Xie
The existence of quasinormal modes (QNMs) for waves propagating on pure de Sitter space has been called into question in several works. We definitively prove the existence of quasi…
The Dirichlet-to-Neumann map for a semilinear wave equation on Lorentzian manifolds
Peter Hintz, Gunther Uhlmann, Jian Zhai
We consider the semilinear wave equation , , on a Lorentzian manifold with timelike boundary. We show that from the knowledge of the Dirichlet-to…
Semiclassical propagation through cone points
Peter Hintz
We introduce a general framework for the study of the diffraction of waves by cone points at high frequencies. We prove that semiclassical regularity propagates through cone points…
Resolvents and complex powers of semiclassical cone operators
Peter Hintz
We give a uniform description of resolvents and complex powers of elliptic semiclassical cone differential operators as the semiclassical parameter tends to . An example of…
A sharp version of Price's law for wave decay on asymptotically flat spacetimes
Peter Hintz
We prove Price's law with an explicit leading order term for solutions of the scalar wave equation on a class of stationary asymptotically flat -dimensional spaceti…
An inverse boundary value problem for a semilinear wave equation on Lorentzian manifolds
Peter Hintz, Gunther Uhlmann, Jian Zhai
We consider an inverse boundary value problem for a semilinear wave equation on a time-dependent Lorentzian manifold with time-like boundary. The time-dependent coefficients of the…
Black hole gluing in de Sitter space
Peter Hintz
We construct dynamical many-black-hole spacetimes with well-controlled asymptotic behavior as solutions of the Einstein vacuum equation with positive cosmological constant. We acco…
Linear stability of slowly rotating Kerr black holes
Dietrich Häfner, Peter Hintz, András Vasy
We prove the linear stability of slowly rotating Kerr black holes as solutions of the Einstein vacuum equation: linearized perturbations of a Kerr metric decay at an inverse polyno…
Normally hyperbolic trapping on asymptotically stationary spacetimes
Peter Hintz
We prove microlocal estimates at the trapped set of asymptotically Kerr spacetimes: these are spacetimes whose metrics decay inverse polynomially in time to a stationary subextrema…
Strong cosmic censorship in charged black-hole spacetimes: still subtle
Vitor Cardoso, Joao L. Costa, Kyriakos Destounis +2
It was recently shown that Strong Cosmic Censorship may be violated in highly charged black-hole spacetimes living in a universe with a positive cosmological constant. Several foll…
Quasinormal modes and Strong Cosmic Censorship
Vitor Cardoso, Joao L. Costa, Kyriakos Destounis +2
The fate of Cauchy horizons, such as those found inside charged black holes, is intrinsically connected to the decay of small perturbations exterior to the event horizon. As such,…
Stability of Minkowski space and polyhomogeneity of the metric
Peter Hintz, András Vasy
We study the nonlinear stability of the -dimensional Minkowski spacetime as a solution of the Einstein vacuum equation. Similarly to our previous work on the stability of co…
Reconstruction of Lorentzian manifolds from boundary light observation sets
Peter Hintz, Gunther Uhlmann
On a time-oriented Lorentzian manifold with non-empty boundary satisfying a convexity assumption, we show that the topological, differentiable, and conformal structure of s…