Global simulations of Minkowski spacetime including spacelike infinity

Abstract

In this work, we study linearised gravitational fields on the entire Minkowski space-time including space-like infinity. The generalised conformal field equations linearised about a Minkowski background are utilised for this purpose. In principle, this conformal representation of Einstein's equations can be used to carry out global simulations of Minkowski space-time. We investigate thoroughly this possibility.

Multiple branches of travelling waves for the Gross–Pitaevskii equation

“…This type of coordinates change has since a long time been assessed in the area of general relativity through the approach of Penrose to conformally map infinite space-time to a finite region through a mapping of the space-time metric [33]. The precise type of compactification that we consider in this work has been successfully applied in the latter context in e.g [18] or in our precise context in [25]. The authors also used them in [15] in order to compute branches of travelling waves solution of the nonlinear Schrödinger equation for various type of nonlinearities.…”

Spectral methods for the spin-2 equation near the cylinder at spatial infinity

“…In future work, we plan to extending the fully spectral code to solve the spin-2 equations globally. A first natural step in this direction is to follow [14] an modify the conformal compactification of the spacetime in order to include the axis of symmetry (here, ρ → ∞). The spectral time evolution should overcome the limitations found in previous works.…”

“…Numerical studies of the spin-2 equations in a neighbourhood of spatial infinity were first presented in [9,10] (first order formulation) and [13] (second order formulation). While the focus was originally on the behaviour of the fields around i 0 , global evolutions were discussed more recently in [14]. These studies provide valuable insight and intuition into the advantages and difficulties of different representations of the critical sets and null infinity.…”

COFFEE—An MPI-parallelized Python package for the numerical evolution of differential equations

“…COFFEE was specifically developed to compute solutions to a system of hyperbolic partial differential equations (PDEs) that represent Friedrich's conformal field equations [2]. It has been used in eight research projects to numerically study the conformal properties of general relativity, [3,4,5,6,7,8,9,10]. As an illustration of the capabilities of COFFEE, in [10] it was used to solve a system of PDEs in the form of an Initial Boundary Value Problem (IBVP) containing 46 variables and 45 constraints on two different high performance clusters using up to 200 processes.…”

“…For example; as Python is an interpreted language syntax can have a large impact on speed of execution (compare for loops to list comprehensions), there are structural issues with interpreted languages (in the case of Python this is the reason for the GIL), additional overhead in the translation of Python script to Python byte code and then to machine instructions, and a lack of the compile time checks that are found in strongly typed languages. Nevertheless the papers [3,4,5,6,7,8,9,10] demonstrate that COFFEE is capable of solving technically challenging and computationally intensive systems of PDEs. Implementation in Python also has advantages.…”