Related papers: Inverse problem for Einstein-scalar field equation…
We prove global Lipschitz stability for inverse source and coefficient problems for first-order linear hyperbolic equations, the coefficients of which depend on both space and time. We use a global Carleman estimate, and a crucial point,…
We present three-dimensional simulations of Einstein equations implementing a symmetric hyperbolic system of equations with dynamical lapse. The numerical implementation makes use of techniques that guarantee linear numerical stability for…
The longitudinal Doppler shift is a measure of hyperbolic distance. Transformations of uniform motion are determined by the Doppler shift, while its square root transforms to a uniformly accelerated frame. A time-velocity space metric is…
We find a one-parameter family of variables which recast the 3+1 Einstein equations into first-order symmetric-hyperbolic form for any fixed choice of gauge. Hyperbolicity considerations lead us to a redefinition of the lapse in terms of an…
The theory presented in this monograph establishes the first mathematically rigorous result on the global nonlinear stability of self-gravitating matter under small perturbations of an asymptotically flat, spacelike hypersurface of…
A spherically symmetric charged ideal fluid solution of Einstein field equation is given in the presence of the cosmological constant and two well known example of this type of solution is presented. If the matter is confined in a region,…
We present a time-dependent solution of the Maxwell equations in the Einstein universe, whose electric and magnetic fields, as seen by the stationary observers, are aligned with the Clifford parallels of the $3$-sphere $S^3$. The conformal…
We present a novel approach for the inverse problem in electrical impedance tomography based on regularized quadratic regression. Our contribution introduces a new formulation for the forward model in the form of a nonlinear integral…
Hybrid inverse problems are mathematical descriptions of coupled-physics (also called multi-waves) imaging modalities that aim to combine high resolution with high contrast. The solution of a high-resolution inverse problem, a first step…
An overview of some recent developments in inhomogeneous models is presented. As the volume and precision of cosmological data improves, it will become more and more essential to understand the non-linear behaviour of the Einstein field…
The 3+1 Hamiltonian formulation in the gauge $D_tN=-K$ on the lapse function fixes the direction of time associated with the trace $K$ of the extrinsic curvature tensor. The Hamiltonian equations hereby become hyperbolic. We study this new…
A formulation of Einstein equations is presented that could yield advantages in the study of collisions of binary compact objects during regimes between linear-nonlinear transitions. The key idea behind this formulation is a separation of…
Interior solutions of Einstein's equations with a non-zero cosmological constant are given for static and spherically symmetric configurations of uniform density. The metric tensor and pressure are determined for both positive and negative…
We introduce a new class of singular partial differential equations, referred to as the second-order hyperbolic Fuchsian systems, and we investigate the associated initial value problem when data are imposed on the singularity. First, we…
An exact solution of the Einstein field equations is found under the assumption of spherically symmetry and the existence of one-parameter group of homothetic motions. This solution has a singularity at $r = 0$, and has non-vanishing…
The paper deals with a special kind of problems that appear in solutions of Einstein's field equations for extended bodies: many structure-dependent terms appear in intermediate calculations that cancel exactly in virtue of the local…
One method of studying the asymptotic structure of spacetime is to apply Penrose's conformal rescaling technique. In this setting, the Einstein equations for the metric and the conformal factor in the unphysical spacetime degenerate where…
In this work we consider the inverse problem of finding guiding pattern shapes that result in desired self-assembly morphologies of block copolymer melts. Specifically, we model polymer self-assembly using Self-Consistent Field Theory and…
This paper is concerned with the problem of scattering of a time-harmonic electromagnetic field by a three-dimensional elastic body. General transmission conditions are considered to model the interaction between the electromagnetic field…
A big-isotropic structure is a generalization of the notion of Dirac structure, due to Vaisman. We discuss the inverse problem of deciding if a vector field is Hamiltonian having a big-isotropic structure as underlying geometry. In [1] we…