On limits of spacetimes -- a coordinate-free approach

TL;DR

This paper introduces a coordinate-free method to analyze the limits of spacetimes, specifically studying Schwarzschild metric limits and discovering new vacuum plane-wave solutions of Petrov type N.

Contribution

It develops a coordinate-free framework for spacetime limits and extends previous results by identifying new Petrov type N limits of Schwarzschild spacetime.

Findings

Schwarzschild limits as mass tends to 0 or ∞ are characterized.

New vacuum plane-wave solutions of Petrov type N are identified as limits.

The approach extends previous understanding of spacetime limits.

Abstract

A coordinate-free approach to limits of spacetimes is developed. The limits of the Schwarzschild metric as the mass parameter tends to 0 or $\infty$ are studied, extending previous results. Besides the known Petrov type D and 0 limits, three vacuum plane-wave solutions of Petrov type N are found to be limits of the Schwarzschild spacetime.