2001/02/06 by Daisuke Ida, Yoshiyuki Morisawa
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Dilaton #Einstein #Geometry #Hypersurface #Mathematical analysis #Mathematical physics #Mathematics #Maxwell's equations #Physics #Symmetry (geometry) #Symmetry group #Transformation (genetics) #gr-qc
paper · pdf · doi:10.1103/physrevd.63.104019
published as Phys.Rev. D63 (2001) 104019 · 5 pages
arxiv created 2001/02/06 · openalex publication_date 2001/04/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
It is shown how to generate three-dimensional Einstein-Maxwell fields from known ones in the presence of a hypersurface-orthogonal, non-null Killing vector field. The continuous symmetry group is isomorphic to the Heisenberg group including the Harrison-type transformation. The symmetry of the Einstein-Maxwell--dilaton system is also studied and it is shown that there is an SL(2,R) transformation between the Maxwell and the dilaton fields. This SL(2,R) transformation is identified with the Geroch transformation of the four-dimensional vacuum Einstein equation in terms of the Ka\luza-Klein mechanism.