Article
Rainich Conditions in (2+1)-Dimensional Gravity
Journal of Mathematical Physics
(2017)
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.Â
Keywords
- General Relativity,
- Gravitation,
- Field Theory,
- Rainich Conditions,
- Electromagnetism,
- Topological Massive Gravity
Disciplines
Publication Date
2017
DOI
https://doi.org/10.1063/1.4974091
Citation Information
Dionisios Krongos and Charles G Torre. "Rainich Conditions in (2+1)-Dimensional Gravity" Journal of Mathematical Physics Vol. 58 (2017) p. 012501 Available at: http://works.bepress.com/charles_torre/91/
Creative Commons license
This work is licensed under a Creative Commons CC_BY-NC International License.