Bona-Mass\'o slices of Reissner-Nordstr\"om spacetimes

TL;DR

This paper investigates Bona-Masso slicing conditions in Reissner-Nordström spacetimes, deriving analytical and numerical solutions for static, spherically symmetric slices, and analyzing their behavior as the charge-to-mass ratio approaches extremality.

Contribution

It provides new analytical and numerical constructions of Bona-Masso slices in charged black hole spacetimes, highlighting their properties and extremal limits.

Findings

Solutions depend on the charge-to-mass ratio λ

Some slices are obtained analytically, others numerically

All slices converge to a unique extremal slice as λ approaches 1

Abstract

Motivated by recent numerical relativity simulations of charged black holes and their interactions, we explore the properties of common slicing conditions in Reissner-Nordstr\"om spacetimes. Specifically, we consider different choices for the so-called Bona-Mass\'o function, and construct static and spherically symmetric slices of the Reissner-Nordstr\"om spacetime satisfying the corresponding slicing conditions. For some of these functions the construction is entirely analytical, while for others we use numerical root-finding to solve quartic equations. Our solutions are parameterized by the charge-to-mass ratio $\lambda = Q/M$ and approach a unique slice, independent of the Bona-Mass\'o functions considered here, in the extremal limit $\lambda \to 1$.