A Method for Calculating the Structure of (Singular) Spacetimes in the Large

TL;DR

This paper introduces a conformal formalism and numerical method to directly compute large-scale spacetime structures, including null infinity and event horizons, in spherically symmetric models with scalar fields.

Contribution

It presents a novel conformal approach and numerical implementation for calculating large-scale spacetime features directly, improving analysis of singularities and radiation.

Findings

Successfully mapped null and timelike infinities to grid points

Determined causal structure of singularities and located event horizons

Extracted radiation and prevented unphysical boundary reflections

Abstract

A formalism and its numerical implementation is presented which allows to calculate quantities determining the spacetime structure in the large directly. This is achieved by conformal techniques by which future null infinity ($\Scri{}^+$) and future timelike infinity ($i^+$) are mapped to grid points on the numerical grid. The determination of the causal structure of singularities, the localization of event horizons, the extraction of radiation, and the avoidance of unphysical reflections at the outer boundary of the grid, are demonstrated with calculations of spherically symmetric models with a scalar field as matter and radiation model.