Constant mean curvature slices in the extended Schwarzschild solution and collapse of the lapse: Part I

TL;DR

This paper provides a detailed analysis of constant mean curvature slices in the Schwarzschild spacetime, demonstrating exponential lapse collapse and calculating the collapse rate.

Contribution

It offers a comprehensive description of CMC foliations in Schwarzschild spacetime and quantifies the lapse collapse rate, advancing understanding of spacetime slicing.

Findings

Lapse collapses exponentially in Schwarzschild spacetime

Explicit computation of the lapse collapse exponent

Detailed characterization of CMC foliations

Abstract

We give a detailed description of the constant mean curvature foliations in the Schwarzschild solution; show that the lapse collapses exponentially, and compute the exponent.