# Spherical symmetry as a test case for unconstrained hyperboloidal evolution II: gauge conditions

## TL;DR

This paper investigates hyperboloidal evolution of a self-gravitating scalar field in spherical symmetry, exploring various gauge conditions and conformal gauges, including null infinity placement, using BSSN and Z4 formulations.

## Contribution

It introduces numerical solutions with flexible gauge conditions and null infinity placement in hyperboloidal evolution, extending previous work by including the option of grid points at null infinity.

## Key findings

- Robust evolutions achieved for various gauge choices.
- Including null infinity in the grid is feasible and effective.
- Different conformal gauges impact the singularity handling.

## Abstract

We present numerical solutions of the hyperboloidal initial value problem for a self-gravitating scalar field in spherical symmetry, using a variety of standard hyperbolic slicing and shift conditions that we adapt to our hyperboloidal setup. We work in the framework of conformal compactification, and study both evolutions that employ the preferred conformal gauge, which simplifies the formal singularities of our equations at null infinity, and evolutions without this simplification. In previous work we have used a staggered grid, which excludes null infinity, while now we include the option of placing a gridpoint directly at null infinity. We use both the generalized BSSN and conformal Z4 formulations of the Einstein equations, study the effect of different gauge conditions, and show that robust evolutions are possible for a range of choices.