The Spherical-Rindler Framework: From Causal Diamonds to Black-Hole and Cosmological Solutions

In this paper, we explore two main aspects of Rindler-type representations. The first concerns transformations of flat spacetime into Rindler-type coordinates, from which two non-trivial families arise: one associated with the standard constant-acceleration curves of the Rindler wedge, and another that covers a compact region of Minkowski spacetime. We detail the properties of these Causal Diamond coordinates and analyze the corresponding observers associated with them. The second aspect of this work, motivated by near-horizon coordinates in the Schwarzschild metric, proposes a novel class of Spherical-Rindler metrics. We demonstrate the utility of this framework by deriving both a black hole solution and a cosmological metric—which naturally emerge from a Spherical-Rindler origin—and contrasting their physical feasibility. We argue that the cosmological solution is the more physically compelling of the two. Finally, we discuss prospective applications for Causal Diamond coordinates in relevant physical scenarios and outline future research directions utilizing Spherical-Rindler metrics.