Embedding initial data for black hole collisions

TL;DR

This paper explores the visualization of initial data for black hole collisions using isometric embedding diagrams, focusing on the Misner geometry and addressing the challenges in constructing these diagrams.

Contribution

It provides an explicit presentation of embedding diagrams for the Misner initial data and discusses partial solutions and related issues.

Findings

Explicit embedding diagrams for Misner data are constructed.

Partial solutions to the embedding problem are presented.

Discussion of challenges in completing the embedding diagrams.

Abstract

We discuss isometric embedding diagrams for the visualization of initial data for the problem of the head-on collision of two black holes. The problem of constructing the embedding diagrams is explicitly presented for the best studied initial data, the Misner geometry. We present a partial solution of the embedding diagrams and discuss issues related to completing the solution.