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

TL;DR

This paper introduces a new class of spherical Rindler coordinates that describe compact Minkowski regions and derive black hole and cosmological solutions from this framework, offering fresh geometric insights.

Contribution

It develops novel spherical Rindler coordinate systems and derives new black hole and cosmological solutions from these coordinates.

Findings

Derived a black hole solution from spherical Rindler coordinates.

Constructed a cosmological metric based on the spherical Rindler framework.

Highlighted geometric properties linking accelerated frames to spacetime curvature.

Abstract

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.