Related papers: Hawking Mass Monotonicity for Initial Data Sets
We develop a numerical approach to compute polar parity perturbations within fully relativistic models of black hole systems embedded in generic, spherically symmetric, anisotropic fluids. We apply this framework to study gravitational wave…
Gross-Pitaevskii and Hartree hierarchies are infinite systems of coupled PDEs emerging naturally from the mean field theory of Bose gases. Their solutions are known to be related to an initial value problem, respectively the…
Systems of PDEs comprised of a combination of constraints and evolution equations are ubiquitous in physics. For both theoretical and practical reasons, such as numerical integration, it is desirable to have a systematic understanding of…
In this paper, we are concerned with the weighted elliptic system \begin{equation*} \begin{cases} -\Delta u=|x|^{\beta} v^{\vartheta},\\ -\Delta v=|x|^{\alpha} |u|^{p-1}u, \end{cases}\quad \mbox{in}\;\ \Omega, \end{equation*}where $\Omega$…
We investigate the initial value problem for the Einstein-Euler equations of general relativity under the assumption of Gowdy symmetry on T3, and we construct matter spacetimes with low regularity. These spacetimes admit, both, impulsive…
In this article, we revisit the initial data rigidity theorem of Eichmair, Galloway and Mendes (arxiv:2009.09527). The goal is to strengthen their result by showing that the initial data sets concerned carry a vector field that is lightlike…
The conformal method is a technique for finding Cauchy data in general relativity solving the Einstein constraint equations, and its parameters include a conformal class, a conformal momentum (as measured by a densitized lapse), and a mean…
The Hyperboloidal Foliation Method (introduced by the authors in 2014) is extended here and applied to the Einstein equations of general relativity. Specifically, we establish the nonlinear stability of Minkowski spacetime for…
We develop an abstract theory of flows of geometric $H$-structures, i.e., flows of tensor fields defining $H$-reductions of the frame bundle, for a closed and connected subgroup $H\subset SO(n)$, on any connected and oriented $n$-manifold…
In this paper, we study the large time behavior of solutions to the Cauchy problem for the anisotropic conservation laws in two dimensional space. Without any smallness assumption on the initial data, the decay rates of solutions in $L^2$…
Tentative observations and theoretical considerations have recently led to renewed interest in models of fundamental physics in which certain ``constants'' vary in time. Assuming fixed black hole mass and the standard form of the…
Hawking radiation and black hole thermodynamics are well understood in the frameworks of quantum field theory and general relativity, with contemporary extensions in string theory, AdS/CFT, and loop quantum gravity. However, an open…
Assuming the validity of random matrices for describing the statistics of a closed chaotic quantum system, we study analytically some statistical properties of the S-matrix characterizing scattering in its open counterpart. In the first…
This paper is the first part of a trilogy dedicated to the following problem: given spherically symmetric characteristic initial data for the Einstein-Maxwell-scalar field system with a cosmological constant $\Lambda$, with the data on the…
We compute the analogue Hawking radiation for modes which posses a small wave vector perpendicular to the horizon. For low frequencies, the resulting mass term induces a total reflection. This generates an extra mode mixing that occurs in…
Misner initial data are a standard example of time-symmetric initial data with two apparent horizons. Compact formulae describing such data are presented in the cases of equal or non-equal masses (i.e. isometric or non-isometric horizons).…
Consider the fixed-$\ell$ inverse scattering problem. We show that the zeros of the regular solution of the Schr\"odinger equation, $r_{n}(E)$, which are monotonic functions of the energy, determine a unique potential when the domain of the…
The convergence of polyhomogeneous expansions of zero-rest-mass fields in asymptotically flat spacetimes is discussed. An existence proof for the asymptotic characteristic initial value problem for a zero-rest-mass field with…
A cosmological model in which the primordial perturbations are provided by global monopoles and in which the dark matter is cold has several interesting features. The model is normalized by choosing its single parameter within the bounds…
We consider a class of Fokker--Planck equations with linear diffusion and superlinear drift enjoying a formal Wasserstein-like gradient flow structure with convex mobility function. In the drift-dominant regime, the equations have a finite…