Causal structure of general relativistic spacetimes

TL;DR

This paper reviews recent advances and open questions in the causality of general relativistic spacetimes, focusing on singularities, horizons, and the structure of causal boundaries.

Contribution

It offers new perspectives on causal boundaries, discusses open problems in horizon stability, and explores the conditions for causality violations in general relativity.

Findings

Overview of Hawking-Penrose singularity theorems

Analysis of horizon stability and energy conditions

Introduction of new causal boundary concepts

Abstract

We present some of the recent results and open questions on the causality problem in General Relativity. The concept of singularity is intimately connected with future trapped surface and inner event horizon formation. We offer a brief overview of the Hawking Penrose singularity theorems and discuss a few open problems concerning the future Cauchy development (domain of dependence), breakdown criteria and energy conditions for the horizon stability. A key question is whether causality violating regions, generating a Cauchy horizon are allowed. We raise several questions concerning the invisibility and stability of closed trapped surfaces from future null infinity and derive the imprisonment conditions. We provide an new perspective of the causal boundaries and spacelike conformal boundary extensions for time oriented Lorentzian manifolds and more exotic settings.