Related papers: Hyperboloidal evolution for scalar scattering in M…
We study corotational wave maps from $(1+4)$-dimensional Minkowski space into the $4$-sphere. We prove the stability of an explicitly known self-similar wave map under perturbations that are small in the critical Sobolev space.
This article describes the theoretical foundation of and explicit algorithms for a novel approach to morphology and anisotropy analysis of complex spatial structure using tensor-valued Minkowski functionals, the so-called Minkowski tensors.…
There does not exist a notion of time which could be transferred straightforwardly from classical to quantum gravity. For this reason, a method of time quantification which would be appropriate for gravity quantization is being sought. One…
A particular, yet relevant, particular case of the Penrose inequality involves null shells propagating in the Minkowski spacetime. Despite previous claims in the literature, the validity of this inequality remains open. In this paper we…
This paper concerns the global theory of properly embedded spacelike surfaces in three-dimensional Minkowski space in relation to their Gaussian curvature. We prove that every regular domain which is not a wedge is uniquely foliated by…
Strategies to model the inspiral, merger and ringdown gravitational waveform of coalescing binaries are restricted in parameter space by the coverage of available numerical-relativity simulations. When more numerical waveforms become…
The Good-Bad-Ugly-F model is a system of semi-linear wave equations that mimics the asymptotic form of the Einstein field equations in generalized harmonic gauge with specific constraint damping and suitable gauge source functions. These…
Scattering of time-harmonic plane wave by two parallel semi-infinite rows, but with staggered edges, is considered on square lattice. The condition imposed on the semi-infinite rows is a discrete analogue of Neumann boundary condition. A…
Motivated by the gauge/gravity duality, we introduce a numerical scheme based on generalized harmonic evolution to solve the Einstein field equations on asymptotically anti-de Sitter (AdS) spacetimes. We work in global AdS5, which can be…
BMS symmetries have been attracting a great deal of interest in recent years. Originally discovered as being the symmetries of asymptotically flat spacetime geometries at null infinity in General Relativity, BMS symmetries have also been…
In [7] Klainerman introduced the hyperboloidal method to prove the global existence results for nonlinear Klein-Gordon equations by using commuting vector fields. In this paper, we extend the hyperboloidal method from Minkowski space to…
An existence and stability result for a class of purely radiative vacuum spacetimes arising from hyperboloidal data is given. This result generalises semiglobal existence results for Minkowski-like spacetimes to the case where the reference…
We revise the use of 8-dimensional conformal, complex (Cartan) domains as a base for the construction of conformally invariant quantum (field) theory, either as phase or configuration spaces. We follow a gauge-invariant Lagrangian approach…
We investigate multiple scattering of scalar waves by an ensemble of $N$ resonant point scatterers in three dimensions. For up to $N = 21$ scatterers, we numerically optimize the positions of the individual scatterers, such as to maximize…
We study the effect of discrete symmetry breaking in inhomogeneous scattering media within the framework of generic wave propagation. Our focus is on one-dimensional scattering potentials exhibiting local symmetries. We find a class of…
The focusing cubic wave equation in three spatial dimensions has the explicit solution $\sqrt{2}/t$. We study the stability of the blowup described by this solution as $t \to 0$ without symmetry restrictions on the data. Via the conformal…
We consider the scalar wave equation $\square_g \phi$ and the linearized Einstein-scalar field system around generalized Kasner spacetimes with spatial topology $\mathbb{T}^D$. In suitable regimes for the Kasner exponents, it is known that…
The dual conformal box integral in Minkowski space is not fully determined by the conformal invariants $z$ and $\bar{z}$. Depending on the kinematic region its value is on a 'branch' of the Bloch-Wigner function which occurs in the…
In this study, we present an analytical investigation of the superradiant scattering of a massive charged conformally coupled scalar field in rotating charged $de~Sitter$ black hole spacetimes within two gravitational theories: General…
Existence and uniqueness in ${\Bbb R}^{n,1}$ of entire spacelike hypersurfaces contained in the future of the origin $O$ and asymptotic to the light-cone, with scalar curvature prescribed at their generic point $M$ as a negative function of…