Related papers: Non-linear numerical Schemes in General Relativity
Here we prove a global existence theorem for the solutions of the semi-linear wave equation with critical non-linearity admitting a positive definite Hamiltonian. Formulating a parametrix for the wave equation in a globally hyperbolic…
In this article, it is shown how the extended conformal Einstein field equations and a gauge based on the properties of conformal geodesics can be used to analyse the non-linear stability of de Sitter-like spacetimes with spatial sections…
The characteristic Cauchy problem of the Einstein field equations has been recently addressed from a completely abstract viewpoint by means of hypersurface data and, in particular, via the notion of double null data. However, this…
This thesis is framed within the field of Mathematical Relativity and is organized into six chapters. After an introduction to the topic in Chapter 1, Chapter 2 reviews and further develops the formalism of hypersurface data, which provides…
We study the properties of the outgoing gravitational wave produced when a non-spinning black hole is excited by an ingoing gravitational wave. Simulations using a numerical code for solving Einstein's equations allow the study to be…
An unsteady problem is considered for a space-fractional diffusion equation in a bounded domain. A first-order evolutionary equation containing a fractional power of an elliptic operator of second order is studied for general boundary…
We present SphericalNR, a new framework for the publicly available Einstein Toolkit that numerically solves the Einstein field equations coupled to the equations of general relativistic magnetohydrodynamics (GRMHD) in a 3+1 split of…
In this article, we study the coupling of the Einstein field equations of general relativity to a family of models of nonlinear electromagnetic fields. The family comprises all covariant electromagnetic models that satisfy the following…
We are interested in the global dynamics of a massive scalar field evolving under its own gravitational field and, in this paper, we study spherically symmetric solutions to Einstein's field equations coupled with a Klein-Gordon equation…
We present a new hybrid Cauchy-characteristic evolution method that is particularly suited for the study of gravitational collapse in spherically-symmetric asymptotically (global) Anti-de Sitter (AdS) spacetimes. The Cauchy evolution allows…
Using the matrix Riemann-Hilbert factorization approach for nonlinear evolution systems which take the form of Lax-pair isospectral deformations and whose corresponding Lax operators contain both discrete and continuous spectra, the…
We present, to the best of our knowledge, the first complete three-dimensional numerical solutions to a broad range of boundary value problems for a general theory of finite strain gradient elasticity. We have chosen for our work, Toupin's…
In this article, we develop an intuitive and efficient, numerical technique to solve the quantum evolution equation of generic lattice-refined models in loop quantum cosmology. As an application of this method, we extensively study the…
By employing the Bianchi identities for the Riemann tensor in conjunction with the Einstein equations, we construct a first order symmetric hyperbolic system for the evolution part of the Cauchy problem of general relativity. In this…
We analyze the Cauchy problem for the vacuum Einstein equations with data on a complete light-cone in an asymptotically Minkowskian space-time. We provide conditions on the free initial data which guarantee existence of global solutions of…
In the mathematical physics literature, there are heuristic arguments, going back three decades, suggesting that for an open set of initially smooth solutions to the Einstein-vacuum equations in high dimensions, stable, approximately…
Strong field (exact) solutions of the gravitational field equations of General Relativity in the presence of a Cosmological Constant are investigated. In particular, a full exact solution is derived within the inhomogeneous Szekeres-Szafron…
We establish the existence and find the necessary and sufficient conditions for a new class of solutions of Locally Rotationally Symmetric spacetimes that have non vanishing rotation and spatial twist simultaneously. We transparently show…
The intimate relations between Einstein's equation, conformal geometry, geometric asymptotics, and the idea of an isolated system in general relativity have been pointed out by Penrose many years ago. A detailed analysis of the interplay of…
In this thesis we consider several aspects of general relativity relating to exact solutions of the Einstein equations. In the first part gravitational plane waves in the Rosen form are investigated, and we develop a formalism for writing…