相关论文: Hyperboloidal Slices and Artificial Cosmology for …

Hyperboloidal slices are spacelike slices that reach future null infinity. Their asymptotic behaviour is different from Cauchy slices, which are traditionally used in numerical relativity simulations. This work uses free evolution of the…

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…

Gravitational radiation and some global properties of spacetimes can only be unambiguously measured at future null infinity . This motivates the interest in reaching it within simulations of coalescing compact objects, whose waveforms are…

We discuss a gauge choice which allows us to avoid the introduction of artificial timelike outer boundaries in numerical studies of test fields based on a 3+1 decomposition of asymptotically flat background spacetimes. The main idea is to…

This is a study of the behavior of wave equations in conformally compactified spacetimes suited to the use of computational boundaries beyond Scri+. There light cones may be adjusted for computational convenience and/or Scri+ may be…

This talk reports on recent progress toward the semiglobal study of asymptotically flat spacetimes within numerical relativity. The development of a 3D solver for asymptotically Minkowski-like hyperboloidal initial data has rendered…

We study the numerical propagation of waves through future null infinity in a conformally compactified spacetime. We introduce an artificial cosmological constant, which allows us some control over the causal structure near null infinity.…

We present the first stable dynamical numerical evolutions of the Einstein equations in terms of a conformally rescaled metric on hyperboloidal hypersurfaces extending to future null infinity. Axisymmetry is imposed in order to reduce the…

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,…

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…

We investigate the use of asymptotically null slices combined with stretching or compactification of the radial coordinate for the numerical simulation of asymptotically flat spacetimes. We consider a 1-parameter family of coordinates…

We study the scalar, conformally invariant wave equation on a four-dimensional Minkowski background in spherical symmetry, using a fully pseudospectral numerical scheme. Thereby, our main interest is in a suitable treatment of spatial…

We present the numerical implementation of a clean solution to the outer boundary and radiation extraction problems within the 3+1 formalism for hyperbolic partial differential equations on a given background. Our approach is based on…

We develop a time-domain numerical framework for global scalar wave scattering in Minkowski spacetime. The main contribution is an exact conformal matching of three compactified regions: a past hyperboloidal domain attached to $\mathscr…

We consider the global evolution problem for Einstein's field equations in the near-Minkowski regime and study the long-time dynamics of a massive scalar field evolving under its own gravitational field. We establish the existence of a…

With the example of the spherically symmetric scalar wave equation on Minkowski space-time we demonstrate that a fully pseudospectral scheme (i.e. spectral with respect to both spatial and time directions) can be applied for solving…

We present new results from two open source codes, using finite differencing and pseudo-spectral methods for the wave equations in (3+1) dimensions. We use a hyperboloidal transformation which allows direct access to null infinity and…

It has recently been demonstrated (Class. Quantum Grav. 31, 085010, 2014) that the conformally invariant wave equation on a Minkowski background can be solved with a fully pseudospectral numerical method. In particular, it is possible to…

We study the ``hyperboloidal Cauchy problem'' for linear and semi-linear wave equations on Minkowski space-time, with initial data in weighted Sobolev spaces allowing singular behaviour at the boundary, or with polyhomogeneous initial data.…

It is well-known that future timelike infinity ($i^+$) in four-dimensional Minkowski spacetime is conformal to the unit three-dimensional hyperboloid ($H^3$). We asymptotically expand massive fields with spin $0,1,2$ near $i^+$ and…