2002/01/31 by Mauricio Cataldo · 51 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Duality (order theory) #Einstein #Einstein tensor #Electric field #Electromagnetic field #Electromagnetic tensor #Field (mathematics) #Geometry #Gravitation #Gravitational field #Linearized gravity #Magnetic field #Magnetostatics #Mathematics #Mathematics of general relativity #Maxwell's equations #Maxwell's equations in curved spacetime #Numerical relativity #Physics #Quantum mechanics #Riemann curvature tensor #Scalar (mathematics) #Spacetime #Superposition principle #gr-qc
paper · pdf · doi:10.1016/s0370-2693(02)01188-7
published in Physics Letters B 529(1-2), 143-149 (Elsevier BV) · 5 pages, Final version
openalex publication_date 2002/03/01 · arxiv created 2002/04/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The fundamental metrics, which describe any static three-dimensional Einstein-Maxwell spacetime (depending only on a unique spacelike coordinate), are found. In this case there are only three independent components of the electromagnetic field: two for the vector electric field and one for the scalar magnetic field. It is shown that we can not have any superposition of these components of the electric and magnetic fields in this kind of static gravitational field. One of the electrostatic Einstein-Maxwell solutions is related to the magnetostatic solution by a duality mapping, while the second electrostatic gravitational field must be solved separately. Solutions induced by the more general (2+1)-Maxwell tensor on the static cylindrically symmetric spacetimes are studied and it is shown that all of them are also connected by duality mappings.