Peter Hintz
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View article: Microlocal analysis near null infinity in asymptotically flat spacetimes
Microlocal analysis near null infinity in asymptotically flat spacetimes Open
View article: The asymptotic behavior of simple eigenvalues of particle-in-well systems
The asymptotic behavior of simple eigenvalues of particle-in-well systems Open
The particle in a well in dimension one is a classical problem in quantum mechanics. We study higher-dimensional analogues of the problem, where the well is a smooth domain in $\mathbb{R}^d$. We show that simple eigenvalues and eigenfuncti…
View article: Conditional non-linear stability of Kerr-de Sitter spacetimes in the full subextremal range
Conditional non-linear stability of Kerr-de Sitter spacetimes in the full subextremal range Open
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 assumption that mode stability holds for these spacetimes. The…
View article: Linear stability of Kerr black holes in the full subextremal range
Linear stability of Kerr black holes in the full subextremal range Open
We prove, unconditionally, the linear stability of the Kerr family in the full subextremal range. On an analytic level, our proof is the same as that of our earlier paper in the slowly rotating case. The additional ingredients we use are, …
View article: Quasinormal modes of near-extremal Reissner-Nordström-de Sitter spacetimes
Quasinormal modes of near-extremal Reissner-Nordström-de Sitter spacetimes Open
We study quasinormal modes (QNMs) for the Klein-Gordon equation on Reissner-Nordström-de Sitter black holes with near-extremal charge. We locate all QNMs of size $\mathcal{O}(κ_{\rm C})$ where $κ_{\rm C}$ is the surface gravity of the Cauc…
View article: Semiclassical propagation through cone points
Semiclassical propagation through cone points Open
View article: Horizons of some asymptotically stationary spacetimes
Horizons of some asymptotically stationary spacetimes Open
On a class of dynamical spacetimes which are asymptotic as $t\to\infty$ to a stationary spacetime containing a horizon $\mathcal{H}_0$, we show the existence of a unique null hypersurface $\mathcal{H}$ which is asymptotic to $\mathcal{H}_0…
View article: Inverse Nonlinear Scattering by a Metric
Inverse Nonlinear Scattering by a Metric Open
We study the inverse problem of determining a time-dependent globally hyperbolic Lorentzian metric from the scattering operator for semilinear wave equations.
View article: Stability of the expanding region of Kerr-de Sitter spacetimes and smoothness at the conformal boundary
Stability of the expanding region of Kerr-de Sitter spacetimes and smoothness at the conformal boundary Open
We give a new proof of the recent result by Fournodavlos-Schlue on the nonlinear stability of the expanding region of Kerr-de Sitter spacetimes as solutions of the Einstein vacuum equations with positive cosmological constant. Our gauge is…
View article: Gluing small black holes along timelike geodesics II: uniform analysis on glued spacetimes
Gluing small black holes along timelike geodesics II: uniform analysis on glued spacetimes Open
Given a smooth globally hyperbolic $(3+1)$-dimensional spacetime $(M,g)$ satisfying the Einstein vacuum equations (possibly with cosmological constant) and an inextendible timelike geodesic $\mathcal{C}$, we constructed in Part I a family …
View article: Pseudodifferential operators on manifolds with scaled bounded geometry
Pseudodifferential operators on manifolds with scaled bounded geometry Open
We prove a general black box result which produces algebras of pseudodifferential operators (ps.d.o.s) on noncompact manifolds, together with a precise principal symbol calculus. Our construction (which also applies in parameter-dependent …
View article: Gluing small black holes along timelike geodesics III: construction of true solutions and extreme mass ratio mergers
Gluing small black holes along timelike geodesics III: construction of true solutions and extreme mass ratio mergers Open
Given a smooth globally hyperbolic $(3+1)$-dimensional spacetime $(M,g)$ satisfying the Einstein vacuum equations (possibly with cosmological constant) and an inextendible timelike geodesic $\mathcal{C}$, we construct, on any compact subse…
View article: The linearized Einstein equations with sources
The linearized Einstein equations with sources Open
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 that the vanishing of appropriate charges of the source, d…
View article: Mode stability and shallow quasinormal modes of Kerr–de Sitter black holes away from extremality
Mode stability and shallow quasinormal modes of Kerr–de Sitter black holes away from extremality Open
A Kerr–de Sitter black hole is a solution (M,g_{\Lambda,\mathfrak{m},\mathfrak{a}}) of the Einstein vacuum equations with cosmological constant \Lambda>0 . It describes a black hole with mass \mathfrak{m}>0 and specific angular momentum \m…
View article: Local theory of wave equations with timelike curves of conic singularities
Local theory of wave equations with timelike curves of conic singularities Open
We develop a general theory for the existence, uniqueness, and higher regularity of solutions to wave-type equations on Lorentzian manifolds with timelike curves of cone-type singularities. These singularities may be of geometric type (con…
View article: Gluing Small Black Holes into Initial Data Sets
Gluing Small Black Holes into Initial Data Sets Open
We prove a strong localized gluing result for the general relativistic constraint equations (with or without cosmological constant) in $$n\ge 3$$ spatial dimensions. We glue an $$\epsilon $$ -rescaling of an asymptotically flat data…
View article: Universality of the quantum energy flux at the inner horizon of asymptotically de Sitter black holes
Universality of the quantum energy flux at the inner horizon of asymptotically de Sitter black holes Open
Recently, it was found that the energy flux of a free scalar quantum field on a Reissner–Nordström–de Sitter spacetime has a quadratic divergence towards the inner horizon of the black hole. Moreover, the leading divergence was found to be…
View article: Correction to: Linear stability of slowly rotating Kerr black holes
Correction to: Linear stability of slowly rotating Kerr black holes Open
View article: Asymptotically de Sitter metrics from scattering data in all dimensions
Asymptotically de Sitter metrics from scattering data in all dimensions Open
In space–time dimensions , we show the existence of solutions of the Einstein vacuum equations which describe asymptotically de Sitter space–times with prescribed smooth data at the conformal boundary. This provides a short alternati…
View article: Recent progress in general relativity
Recent progress in general relativity Open
We review recent progress in general relativity. After a brief introduction to some of the key analytical and geometric features of the Einstein equations, we focus on two main developments: the stability of black hole solutions, and the f…
View article: Asymptotically de Sitter metrics from scattering data in all dimensions
Asymptotically de Sitter metrics from scattering data in all dimensions Open
In spacetime dimensions $n+1\geq 4$, we show the existence of solutions of the Einstein vacuum equations which describe asymptotically de Sitter spacetimes with prescribed smooth data at the conformal boundary. This provides a short altern…
View article: Universality of the quantum energy flux at the inner horizon of asymptotically de Sitter black holes
Universality of the quantum energy flux at the inner horizon of asymptotically de Sitter black holes Open
Recently, it was found that the energy flux of a free scalar quantum field on a Reissner-Nordström-de Sitter spacetime has a quadratic divergence towards the inner horizon of the black hole. Moreover, the leading divergence was found to be…
View article: Exterior Stability of Minkowski Space in Generalized Harmonic Gauge
Exterior Stability of Minkowski Space in Generalized Harmonic Gauge Open
We give a short proof of the existence of a small piece of null infinity for $$(3+1)$$ -dimensional spacetimes evolving from asymptotically flat initial data as solutions of the Einstein vacuum equations. We introduce a modification…
View article: The linearized Einstein equations with sources
The linearized Einstein equations with sources Open
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 that the vanishing of appropriate charges of the source, d…
View article: Gluing small black holes along timelike geodesics I: formal solution
Gluing small black holes along timelike geodesics I: formal solution Open
Given a smooth globally hyperbolic $(3+1)$-dimensional spacetime satisfying the Einstein vacuum equations (possibly with cosmological constant) and an inextendible timelike geodesic, we construct a family of metrics depending on a small pa…
View article: Microlocal analysis near null infinity in asymptotically flat spacetimes
Microlocal analysis near null infinity in asymptotically flat spacetimes Open
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 dimension. The classes of metrics and wave type operators we co…
View article: Exterior stability of Minkowski space in generalized harmonic gauge
Exterior stability of Minkowski space in generalized harmonic gauge Open
We give a short proof of the existence of a small piece of null infinity for $(3+1)$-dimensional spacetimes evolving from asymptotically flat initial data as solutions of the Einstein vacuum equations. We introduce a modification of the st…
View article: Microlocal analysis of operators with asymptotic translation- and dilation-invariances
Microlocal analysis of operators with asymptotic translation- and dilation-invariances Open
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-invariance, or asymptotic homogeneity with respect to scalin…
View article: Linear waves on asymptotically flat spacetimes. I
Linear waves on asymptotically flat spacetimes. I Open
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 zero energy resonances for a stationary model operator. Our me…
View article: Underdetermined-elliptic PDE on asymptotically Euclidean manifolds, and generalizations
Underdetermined-elliptic PDE on asymptotically Euclidean manifolds, and generalizations Open
We study underdetermined-elliptic linear partial differential operators $P$ on asymptotically Euclidean manifolds, such as the divergence operator on 1-forms or symmetric 2-tensors. Suitably interpreted, these are instances of (weighted) t…