2011/11/11 by Jürgen Dietz, Jill Dietz, Alexander Dirmeier +1
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Classical mechanics #Closed timelike curve #Cosmology and Gravitation Theories #Deriving the Schwarzschild solution #General relativity #Geodesic #Kerr metric #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quantum field theory in curved spacetime #Quantum gravity #Quantum mechanics #Schwarzschild geodesics #Schwarzschild metric #Schwarzschild radius #Solving the geodesic equations #Spacetime #Spacetime topology #Spherically symmetric spacetime #Stationary spacetime #Theoretical physics #gr-qc #math.DG
paper · pdf · doi:10.1016/j.geomphys.2011.11.013
14 pages, 3 figures
arxiv created 2011/11/11 · openalex publication_date 2011/12/07 · arxiv updated 2012/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We formulate the concept of time machine structure for spacetimes exhibiting a compactely constructed region with closed timelike curves. After reviewing essential properties of the pseudo Schwarzschild spacetime introduced by A. Ori, we present an analysis of its geodesics analogous to the one conducted in the case of the Schwarzschild spacetime. We conclude that the pseudo Schwarzschild spacetime is geodesically incomplete and not extendible to a complete spacetime. We then introduce a rotating generalization of the pseudo Schwarzschild metric, which we call the the pseudo Kerr spacetime. We establish its time machine structure and analyze its global properties.