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Rainich Conditions in (2+1)-Dimensional Gravity
arXiv:1611.04143 (2016)
  • Dionisios Krongos
  • Charles G Torre
Abstract
In (3 + 1) spacetime dimensions the Rainich conditions are a set of equations expressed solely in terms of the metric tensor which are equivalent to the Einstein-Maxwell equations for non-null electromagnetic fields. Here we provide the analogous conditions for (2 + 1)-dimensional gravity coupled to electromagnetism. Both the non-null and null cases are treated. The construction of these conditions is based upon reducing the problem to that of gravity coupled to a scalar field, which we have treated elsewhere. These conditions can be easily extended to other theories of (2 + 1)-dimensional gravity. For example, we apply the geometrization conditions to topologically massive gravity coupled to the electromagnetic field and obtain a family of plane-fronted wave solutions. 
Keywords
  • General Relativity,
  • Gravitation,
  • Field Theory,
  • Rainich Conditions,
  • Electromagnetism,
  • Topological Massive Gravity
Publication Date
November 7, 2016
Citation Information
Dionisios Krongos and Charles G Torre. "Rainich Conditions in (2+1)-Dimensional Gravity" arXiv:1611.04143 (2016)
Available at: http://works.bepress.com/charles_torre/91/
Creative Commons license
Creative Commons License
This work is licensed under a Creative Commons CC_BY-NC International License.