Lapse function for maximally sliced Brill-Lindquist initial data

TL;DR

This paper derives an analytic form of the lapse function for binary black holes in maximal slicing, revealing its relation to minimal surfaces in the small mass-to-separation limit.

Contribution

It provides an explicit analytic expression for the lapse function in binary black hole initial data under maximal slicing.

Findings

Lapse function expressed analytically for binary black holes

Zero lapse surface coincides with minimal surfaces in certain limits

Results applicable to initial data in numerical relativity

Abstract

For binary black holes the lapse function corresponding to the Brill-Lindquist initial value solution for uncharged black holes is given in analytic form under the maximal slicing condition. In the limiting case of very small ratio of mass to separation between the black holes the surface defined by the zero value of the lapse function coincides with the minimal surfaces around the singularities.