2017/04/30 by Vangelis Giantsos, Christos G. Tsagas · 3 citations
Physics and Astronomy · #Advanced Differential Geometry Research #Classical mechanics #Cosmology and Gravitation Theories #Field line #Gravitation #Gravitational energy #Magnetic energy #Magnetic field #Magnetization #Physics #Quantum mechanics #Relativity and Gravitational Theory #gr-qc
paper · pdf · doi:10.1093/mnras/stx1919
published in Monthly Notices of the Royal Astronomical Society 472(1), 869-875 (Oxford University Press) · Typos corrected. Published version
openalex publication_date 2017/07/26 · openalex created_date 2017/08/08 · arxiv created 2017/09/27 · arxiv updated 2017/09/28 · openalex updated_date 2026/08/05
We consider the ‘kinematics’ of space-like congruences and apply them to a family of self-gravitating magnetic forcelines. Our aim is to investigate the convergence and the possible focusing of these lines, as well as their rotation and shear deformation. In so doing, we introduce a covariant 1+2 splitting of the 3-D space, parallel and orthogonal to the direction of the field lines. The convergence, or not, of the latter is monitored by a specific version of the Raychaudhuri equation, obtained after propagating the spatial divergence of the unit magnetic vector along its own direction. The resulting expression shows that, although the convergence of the magnetic forcelines is affected by the gravitational pull of all the other sources, it is unaffected by the field's own gravity, irrespective of how strong the latter is. This rather counterintuitive result is entirely due to the magnetic tension, namely to the negative pressure the field exerts parallel to its lines of force. In particular, the magnetic tension always cancels out the field's energy-density input to the Raychaudhuri equation, leaving the latter free of any direct magnetic-energy contribution. Similarly, the rotation and the shear deformation of the aforementioned forcelines are also unaffected by the magnetic input to the total gravitational energy. In a sense, the magnetic lines do not seem to ‘feel’ their own gravitational field no matter how strong the latter may be.