相关论文: Non-linear numerical Schemes in General Relativity

We present results from a new technique which allows extraction of gravitational radiation information from a generic three-dimensional numerical relativity code and provides stable outer boundary conditions. In our approach we match the…

From Einstein's theory we know that besides the electromagnetic spectrum, objects like quasars, active galactic nuclei, pulsars and black holes also generate a physical signal of purely gravitational nature. The actual form of the signal is…

An implicit, fully characteristic, numerical scheme for solving the field equations of a cosmic string coupled to gravity is described. The inclusion of null infinity as part of the numerical grid allows us to apply suitable boundary…

The field equations for a time dependent cylindrical cosmic string coupled to gravity are reformulated in terms of geometrical variables defined on a 2+1-dimensional spacetime by using the method of Geroch decomposition. Unlike the…

We present a new method of extracting gravitational radiation from three-dimensional numerical relativity codes and providing outer boundary conditions. Our approach matches the solution of a Cauchy evolution of Einstein's equations to a…

The demand to obtain answers to highly complex problems within strong-field gravity has been met with significant progress in the numerical solution of Einstein's equations - along with some spectacular results - in various setups. We…

Computational techniques which establish the stability of an evolution-boundary algorithm for a model wave equation with shift are incorporated into a well-posed version of the initial-boundary value problem for gravitational theory in…

This article begins with a brief introduction to numerical relativity aimed at readers who have a background in applied mathematics but not necessarily in general relativity. I then introduce and summarise my work on the problem of treating…

We investigate the numerical stability of Cauchy evolution of linearized gravitational theory in a 3-dimensional bounded domain. Criteria of robust stability are proposed, developed into a testbed and used to study various…

In this work numerical methods for solving Einstein's equations are developed and applied to the study of inhomogeneous cosmological models. A two-dimensional computer code is described which implements two advanced numerical methods:…

In this article, we prove the convergence of a semi-discrete numerical method applied to a general class of nonlocal nonlinear wave equations where the nonlocality is introduced through the convolution operator in space. The most important…

Although the traditional form of the Einstein field equations is intrinsically four-dimensional, the field of numerical general relativity focuses on the reformulation of these equations as a 3 + 1-dimensional Cauchy problem, in which…

I review the development of numerical evolution codes for general relativity based upon the characteristic initial value problem. Progress in characteristic evolution is traced from the early stage of 1D feasibility studies to 2D…

In this paper we demonstrate for the first time that it is possible to solve numerically the Cauchy problem for the linearisation of the general conformal field equations near spacelike infinity, which is only well-defined in Friedrich's…

In this thesis, I present the first numerical scheme able to perform Cauchy evolutions of asymptotically AdS spacetimes with reflective boundary conditions under no symmetry requirements on the solution. The scheme is based on the…

This paper is concerned with giving the proof that there is a general decoupling property of vacuum and nonvacuum gravitational field equations in Einstein gravity and $f(R,T)$-modifications. The constructions are possible in terms of…

This paper gives a detailed pedagogic presentation of the central concepts underlying a new algorithm for the numerical solution of Einstein's equations for gravitation. This approach incorporates the best features of the two leading…

I review the development of numerical evolution codes for general relativity based upon the characteristic initial value problem. Progress is traced from the early stage of 1D feasibility studies to 2D axisymmetric codes that accurately…

This thesis is concerned with global properties of those cosmological solutions of Einstein's field equations which obey accelerated expansion into the future driven by a non-vanishing cosmological constant, as suggested by current…

Numerical relativity is an essential tool for solving Einstein's equations of general relativity for dynamical systems characterized by high velocities and strong gravitational fields. The implementation of new algorithms that can solve…