Causal Structure and Spacetime Singularities

TL;DR

This paper argues that causal structure and measure are more fundamental than the metric in General Relativity, providing a natural framework to understand spacetime singularities like black holes and the Big Bang.

Contribution

It demonstrates that causal structure and measure can remain regular at singularities, suggesting a shift in focus to these aspects for understanding spacetime singularities.

Findings

Causal structure remains well-defined at singularities.

The metric becomes singular while causal structure does not.

A framework based on causal structure better handles singularities.

Abstract

In General Relativity the metric can be recovered from the structure of the lightcones and a measure giving the volume element. Since the causal structure seems to be simpler than the Lorentzian manifold structure, this suggests that it is more fundamental. But there are cases when seemingly healthy causal structure and measure determine a singular metric. Here it is shown that this is not a bug, but a feature, because big-bang and black hole singularities are instances of this situation. But while the metric is special at singularities, being singular, the causal structure and the measure are not special in an explicit way at singularities. Therefore, considering the causal structure more fundamental than the metric provides a more natural framework to deal with spacetime singularities.