A Singular Conformal Spacetime

TL;DR

This paper explores a new singular, maximally-symmetric conformal spacetime arising as a limit of de Sitter solutions, with implications for understanding the early universe's geometry and thermodynamics.

Contribution

It introduces a novel singular cone-space as a maximally-symmetric solution in Einstein's equations, expanding the class of known conformal spacetimes.

Findings

Identifies a new singular conformal spacetime with maximal symmetry.

Analyzes geometric and thermodynamic properties of the cone-space.

Suggests potential relevance to primordial universe models.

Abstract

The infinite cosmological "constant" limit of the de Sitter solutions to Einstein's equation is studied. The corresponding spacetime is a singular, four-dimensional cone-space, transitive under proper conformal transformations, which constitutes a new example of maximally-symmetric spacetime. Grounded on its geometric and thermodynamic properties, some speculations are made in connection with the primordial universe.