1999/07/03 by Akihiro Ishibashi, Akio Hosoya · 3 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Geometry #Gravitational singularity #Mathematical analysis #Mathematical physics #Mathematics #Naked singularity #Operator (biology) #Physics #Quantum mechanics #Scalar (mathematics) #Singularity #Sobolev space #Spacetime #gr-qc
paper · pdf · doi:10.1103/physrevd.60.104028
published as Phys.Rev. D60 (1999) 104028 · 25 pages, 3 figures, Accepted for publication in Phys.Rev.D
arxiv created 1999/07/03 · openalex publication_date 1999/10/26 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
To probe naked spacetime singularities with waves rather than with particles we study the well posedness of initial value problems for test scalar fields with finite energy so that the natural function space of initial data is the Sobolev space. In the case of static and conformally static spacetimes we examine the essential self-adjointness of the time translation operator in the wave equation defined in the Hilbert space. For some spacetimes the classical singularity becomes regular if probed with waves while stronger classical singularities remain singular. If the spacetime is regular when probed with waves we may say that the spacetime is ``globally hyperbolic.''