On a de Sitter-like spacetime with cylindrical symmetry

TL;DR

This paper analyzes a static, de Sitter-like spacetime with cylindrical symmetry, revealing constant curvature invariants, conformal flatness, and horizon properties similar to black holes, driven by a specific stress-energy tensor.

Contribution

It introduces a new de Sitter-like metric with cylindrical symmetry and explores its geometric and thermodynamic properties, including horizon entropy and gravitational energy.

Findings

Curvature invariants are constant everywhere.

Horizon surface gravity equals the parameter .

Horizon entropy follows the Bekenstein-Hawking relation.

Abstract

A curved static de Sitter-like metric is analyzed. The source of curvature is rooted from a constant stress tensor with positive energy density and negative pressures. All the curvature invariants are constant everywhere and the geometry is conformally flat. The horizon surface gravity equals the parameter $\omega$ from the metric that is also interpreted as an angular velocity. The Tolman-Komar gravitational energy is investigated. One finds that the horizon entropy satisfies the relation $S = A_{H}/4$, as for the black hole horizon.