Slicing black hole spacetimes

TL;DR

This paper develops a general framework for analyzing stationary spacelike slicings of stationary spacetimes, especially black holes, to better understand their properties and utility in general relativity.

Contribution

It introduces a unified approach to characterize and categorize slicing conditions in stationary spacetimes, linking geometric properties with their physical and computational usefulness.

Findings

Categorizes various slicing conditions used in black hole spacetimes.

Provides geometric characterizations of slicings based on observer congruences.

Connects slicing choices with initial value and evolution problems in general relativity.

Abstract

A general framework is developed to investigate the properties of useful choices of stationary spacelike slicings of stationary spacetimes whose congruences of timelike orthogonal trajectories are interpreted as the world lines of an associated family of observers, the kinematical properties of which in turn may be used to geometrically characterize the original slicings. On the other hand properties of the slicings themselves can directly characterize their utility motivated instead by other considerations like the initial value and evolution problems in the 3-plus-1 approach to general relativity. An attempt is made to categorize the various slicing conditions or "time gauges" used in the literature for the most familiar stationary spacetimes: black holes and their flat spacetime limit.