Axial Symmetry Cosmological Constant Vacuum Solution of Field Equations with a Curvature Singularity, Closed Time-Like Curves, and Deviation of Geodesics

2019/10/31 by Faizuddin Ahmed, Bidyut Bikash Hazarika, Debojit Sarma
Physics and Astronomy · #Advanced Differential Geometry Research #Axial symmetry #Black Holes and Theoretical Physics #Classical mechanics #Constant curvature #Cosmological constant #Cosmology and Gravitation Theories #Curvature #De Sitter space #De Sitter universe #General relativity #Geodesic #Geometry #Hypersurface #Mathematical analysis #Mathematical physics #Physics #Quantum mechanics #Singularity #Symmetry (geometry) #Universe #Vacuum solution #physics.gen-ph

paper · pdf · doi:10.1155/2020/8265872

published as Adv. High Energy Phys. vol. 2020, Article ID 8265872 (2020) · 17 pages, accepted for publication in Adv. High Energy Physics journal

arxiv created 2020/11/03 · openalex publication_date 2020/11/18 · arxiv updated 2020/11/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In this paper, we present a type D, nonvanishing cosmological constant, vacuum solution of Einstein’s field equations, extension of an axially symmetric, asymptotically flat vacuum metric with a curvature singularity. The space-time admits closed time-like curves (CTCs) that appear after a certain instant of time from an initial space-like hypersurface, indicating it represents a time-machine space-time. We wish to discuss the physical properties and show that this solution can be interpreted as gravitational waves of Coulomb-type propagate on anti-de Sitter space backgrounds. Our treatment focuses on the analysis of the equation of geodesic deviations.

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