Bona-Masso slicing conditions and the lapse close to black-hole punctures

TL;DR

This paper analyzes Bona-Masso slicing conditions near black-hole punctures, deriving analytical lapse expressions and demonstrating improved numerical performance with certain function choices in spectral simulations.

Contribution

It introduces generalized Bona-Masso functions that yield a lapse proportional to radius near punctures and validates their effectiveness through analytical and numerical analysis.

Findings

Analytical lapse expressions near black-hole punctures

Generalized functions improve numerical stability

Lapse proportional to radius enhances spectral simulation accuracy

Abstract

We consider several families of functions $f(\alpha)$ that appear in the Bona-Masso slicing condition for the lapse function $\alpha$. Focusing on spherically symmetric and time-independent slices we apply these conditions to the Schwarzschild spacetime in order to construct analytical expressions for the lapse $\alpha$ in terms of the areal radius $R$. We then transform to isotropic coordinates and determine the dependence of $\alpha$ on the isotropic radius $r$ in the vicinity of the black-hole puncture. We propose generalizations of previously considered functions $f(\alpha)$ for which, to leading order, the lapse is proportional to $r$ rather than a non-integer power of $r$. We also perform dynamical simulations in spherical symmetry and demonstrate advantages of the above choices in numerical simulations employing spectral methods.