Semiglobal Numerical Calculations of Asymptotically Minkowski Spacetimes

TL;DR

This paper discusses recent advances in numerical relativity for simulating asymptotically flat spacetimes, focusing on a new 3D solver for hyperboloidal initial data and its application to studying the entire future evolution of such spacetimes.

Contribution

Development of a 3D solver for hyperboloidal initial data enabling the application of Friedrich's conformal field equations to asymptotically Minkowski spacetimes.

Findings

Successful simulation of the entire future of weak initial data including null and timelike infinity

Demonstration of the numerical techniques and capabilities of the new solver

Implications for future research in numerical relativity and spacetime modeling

Abstract

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 possible the application of Friedrich's conformal field equations to astrophysically interesting spacetimes. As a first application, the whole future of a hyperboloidal set of weak initial data has been studied, including future null and timelike infinity. Using this example we sketch the numerical techniques employed and highlight some of the unique capabilities of the numerical code. We conclude with implications for future work.