Geometry of Black Holes and Multi-Black-Holes in 2+1 dimensions

TL;DR

This paper explores the geometry and initial value formulation of black holes and multi-black-hole configurations in 2+1 dimensions, including their time evolution and angular momentum aspects.

Contribution

It provides a detailed analysis of black hole geometries, initial conditions, and dynamics in 2+1 dimensions, extending understanding of multi-black-hole systems and their analogies to higher dimensions.

Findings

Characterization of single and multi-black-hole initial data

Description of time evolution using Raychaudhuri equation

Analysis of black holes with angular momentum in 2+1 dimensions

Abstract

Lecture given at ``Raychaudhuri session," ICGC-95 conference, Pune (India), December 1995. Contents: I. Introduction II. (2+1)-Dimensional Initial Values in Stereographic Projection A. The single, non-rotating black hole B. Non-rotating multi-black-holes C. ``Black Hole" Universe Initial Values III. Time Development: Enter the Raychaudhuri Equation IV. Time Development in Stereographic Projection A. The BTZ black hole spacetime B. Multi-Black-Hole Spacetimes V. Black Holes with Angular Momentum VI. Analogous 3+1-Dimensional Black Holes VII. Conclusions