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Departamento de Gravitación y Teoría de CamposSeminarios 2010 |
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Instituto de Ciencias Nucleares, UNAM |
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Departamento de Gravitación y Teoría de CamposSeminarios 2010 |
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Instituto de Ciencias Nucleares, UNAM |
Jueves 11 de Marzo, a las 17:30 hrs en el Auditorio Principal del ICN
Mercedes Velazquez (CINVESTAV)
BF gravity with Immirzi parameter and cosmological constant
| General relativity expressed as a constrained BF theory was given by Plebanski many years ago. The basic idea behind Plebanski's formulation is that the fundamental variables for describing the gravitational field (general relativity) are neither a metric (as it is in the Einstein-Hilbert action) nor a tetrad together with a Lorentz connection (as it is in the Palatini action), but two-form fields, a connection a 1-form, and some Lagrange multipliers. This view point has been adopted in the construction of other action principles, which also express general relativity as a constrained BF theory. The link with tetrad gravity is made by solving the constraints for the two-form fields which amounts to express the B's in terms of tetrad fields. In particular, a formulation for real general relativity expressed as a constrained BF theory that involves the Immirzi parameter was given in by Capovilla, Montesinos, Prieto, and Rojas. We modify this theory in order to allow the inclusion of the cosmological constant. The resulting action principle is on the same footing as the original Plebanski action in the sense that the equations of motion coming from the new action principle are equivalent to the Holst action principle plus a cosmological constant without the need of imposing additional restrictions on the fields. We consider this result a relevant step towards the coupling of matter fields to gravity in the framework of the CMPR action principle. |
