Related papers: Computing Gowdy spacetimes via spectral evolution …
We study the dynamics of a bounded gravitational collapsing configuration emitting gravitational waves, where the exterior spacetime is described by Robinson-Trautman geometries. The full nonlinear regime is examined by using the Galerkin…
The paper introduces a method to solve inverse problems for hyperbolic systems where the leading order terms are non-linear. We apply the method to the coupled Einstein-scalar field equations and study the question whether the structure of…
The description of the universe evolving in time according to general relativity is given in comparison with the quantum description of the same universe in terms of semiclassical wave functions. The spacetime geometry is determined by the…
We present a general abstract framework for the systematic numerical approximation of dissipative evolution problems. The approach is based on rewriting the evolution problem in a particular form that complies with an underlying energy or…
In the previous works [I. Rodnianski and Y. Shlapentokh-Rothman, Naked Singularities for the Einstein Vacuum Equations: The Exterior Solution, arXiv:1912.08478 and Y. Shlapentokh-Rothman, Naked Singularities for the Einstein Vacuum…
This thesis is concerned with the development and application of conformal techniques to numerical calculations of asymptotically flat spacetimes. The conformal compactification technique enables us to calculate spatially unbounded domains,…
We study the stability of three-dimensional numerical evolutions of the Einstein equations, comparing the standard ADM formulation to variations on a family of formulations that separate out the conformal and traceless parts of the system.…
This is the first of a series of papers describing a numerical implementation of the conformally rescaled Einstein equation, an implementation designed to calculate asymptotically flat spacetimes, especially spacetimes containing black…
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…
We consider Stokes' conjecture concerning the shape of the extremal two-dimensional water wave. By new geometric methods including a nonlinear frequency formula, we prove Stokes' conjecture in the original variables. Our results do not rely…
To explore the properties of space and initial singularities in the context of general relativity, where spacetime becomes poorly defined and no longer belongs to a regular manifold, we examine the evolution of the expansion of timelike…
The linearly polarized Gowdy $T^3$ model can be regarded as compact Bianchi I cosmologies with inhomogeneous modes allowed to travel in one direction. We study a hybrid quantization of this model that combines the loop quantization of the…
This paper proves that, in a four-dimensional spherically symmetric spacetime manifold, one can consider coordinate transformations expressed by fractional linear maps which give rise to isometries and are the simplest example of coordinate…
We study homogeneous and isotropic cosmologies in a Weyl spacetime. We show that for homogeneous and isotropic spacetimes, the field equations can be reduced to the Einstein equations with a two-fluid source. We write the equations as a…
We present an efficient numerical code based on spectral methods to integrate the field equations of general Robinson-Trautmann spacetimes. The most natural basis functions for the spectral expansion of the metric functions are spherical…
A new numerical scheme to solve the Einstein field equations based upon the generalized harmonic decomposition of the Ricci tensor is introduced. The source functions driving the wave equations that define generalized harmonic coordinates…
Current spectral simulations of Einstein's equations require writing the equations in first-order form, potentially introducing instabilities and inefficiencies. We present a new penalty method for pseudo-spectral evolutions of second order…
We review recent efforts to re-formulate the Einstein equations for fully relativistic numerical simulations. The so-called numerical relativity (computational simulations in general relativity) is a promising research field matching with…
Two classes of stationary axisymmetric solutions of Einstein's equations for isolated differentially rotating matter sources are presented. The asymptotic regime is extracted, with attention to quasilocal gravitational energy, shear and…
Several applications of spectral methods to problems related to the relativistic astrophysics of compact objects are presented. Based on a proper definition of the analytical properties of regular tensorial functions we have developed a…