# Slicing conditions for axisymmetric gravitational collapse of Brill waves

## TL;DR

This paper introduces a new 'quasi-maximal' slicing condition for numerical relativity that improves the evolution of near-critical Brill wave data, outperforming traditional gauges in stability and behavior.

## Contribution

A novel slicing condition based on 1+log slicing with an added source term from maximal slicing, enhancing numerical stability for Brill wave simulations.

## Key findings

- The new slicing condition demonstrates improved stability for near-critical Brill wave evolutions.
- Constructed spacetimes show black holes settling into Schwarzschild solutions.
- Gauge-independent quantities confirm the robustness of the new method.

## Abstract

In numerical relativity, spacetimes involving compact strongly gravitating objects are constructed as numerical solutions of Einstein's equations. Success of such a process strongly depends on the availability of appropriate coordinates, which are typically constructed dynamically. A very robust coordinate choice is a so-called moving puncture gauge, commonly used for numerical simulations of black hole spacetimes. Nevertheless it is known to fail for evolving near-critical Brill wave data. We construct a new `quasi-maximal' slicing condition and demonstrate that it exhibits better behavior for such data. This condition is based on the 1+log slicing with an additional source term derived from maximal slicing. It is relatively simple to implement in existing moving puncture codes and computationally inexpensive. We also illustrate the properties of constructed spacetimes based on gauge-independent quantities in compactified spacetime diagrams. These invariants are also used to show how created black holes settle down to a Schwarzschild black hole.