Edgar Alejandro León

arXiv2026

Mapping Schwarzschild Spacetime: From Kruskal to Diamond and Golden Representations

We present several representations of the Schwarzschild spacetime. Some of these are classical, such as the embedding, Tortoise, and Kruskal representations. The latter two motivate the introduction of pulsating coordinates (or the Diamond representation), a compact approach recently proposed for spherically symmetric static metrics. We then introduce the Golden representation for the Schwarzschild spacetime, where what we call the Fibonacci metric, and the golden ratio, become ubiquitous. We conclude by offering some visual and physical interpretations of this approach.

gr-qc↗

arXiv2026

The Spherical-Rindler framework: From compact Minkowski regions to black-Hole and cosmological Solutions

In this article we first develop novel Rindler-type representations of flat spacetime by demonstrating that the standard hyperbolic transformation is a member of an infinite family of coordinate mappings. We specifically introduce cyclic coordinates, which, in contrast to the conventional Rindler wedge, delineate a compact region of Minkowski spacetime. By extending this framework, and motivated by near horizon coordinates in Schwarzschild metric, we propose a class of Spherical Rindler metrics. We demonstrate the utility of this approach by deriving and analyzing a black hole solution and a cosmological metric, both emerging naturally from a Spherical Rindler origin. Our results highlight unique geometric properties of these solutions, providing new insights into the relationship between accelerated frames and global spacetime curvature.

gr-qc↗