Note on flat foliations of spherically symmetric spacetimes

TL;DR

This paper presents a straightforward method using Hamiltonian constraints to identify flat spacelike foliations in spherically symmetric spacetimes, providing explicit formulas for their extrinsic curvatures.

Contribution

It introduces a simple, Hamiltonian-based approach to find flat foliations in spherically symmetric spacetimes, with explicit extrinsic curvature formulas.

Findings

Flat spacelike foliations exist in spherically symmetric spacetimes.

Explicit formulas for extrinsic curvatures of these foliations are derived.

The method simplifies understanding of spacetime slicing in general relativity.

Abstract

It is known that spherically symmetric spacetimes admit flat spacelike foliations. We point out a simple method of seeing this result via the Hamiltonian constraints of general relativity. The method yields explicit formulas for the extrinsic curvatures of the slicings.