Ideal points, directed completion and the case of the maximally extended Schwarzschild spacetime

Nicola Gigli; Argam Ohanyan; Marco Picerni; Zhe-Feng Xu; Matteo Zanardini

Ideal points, directed completion and the case of the maximally extended Schwarzschild spacetime

Differential Geometry 2026-08-05 v1 General Relativity and Quantum Cosmology

Authors: Nicola Gigli , Argam Ohanyan , Marco Picerni , Zhe-Feng Xu , Matteo Zanardini

Abstract

We study the directed completion of Lorentzian pre-length spaces, and we show that, under some natural assumptions which cover the case of smooth globally hyperbolic spacetimes, it coincides with the future causal completion of Geroch--Kronheimer--Penrose. Moreover, we provide applications of our findings by characterizing the directed completion of the Kruskal--Szekeres spacetime in terms of its radial null geodesics.

Keywords

Lorentzian pre-length spaces directed completion causal completion Kruskal-Szekeres spacetime radial null geodesics globally hyperbolic spacetimes

Cite

@article{arxiv.2608.04718,
  title  = {Ideal points, directed completion and the case of the maximally extended Schwarzschild spacetime},
  author = {Nicola Gigli and Argam Ohanyan and Marco Picerni and Zhe-Feng Xu and Matteo Zanardini},
  journal= {arXiv preprint arXiv:2608.04718},
  year   = {2026}
}

Comments

26 pages, 1 figure