3+1 geodesic equation and images in numerical spacetimes

TL;DR

This paper derives 3+1 formalism geodesic equations for null and timelike particles, enabling accurate ray-tracing in numerical spacetimes to produce images and spectra of neutron stars and black hole formation.

Contribution

It introduces a 3+1 framework for geodesic equations including energy evolution and redshift, facilitating image and spectrum computation in numerical relativity.

Findings

Generated images of stationary neutron stars.

Simulated spectra during neutron star collapse.

Demonstrated ray-tracing in dynamical spacetimes.

Abstract

The equations governing null and timelike geodesics are derived within the 3+1 formalism of general relativity. In addition to the particle's position, they encompass an evolution equation for the particle's energy leading to a 3+1 expression of the redshift factor for photons. An important application is the computation of images and spectra in spacetimes arising from numerical relativity, via the ray-tracing technique. This is illustrated here by images of numerically computed stationary neutron stars and dynamical neutron stars collapsing to a black hole.