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We present a new B F-type action for complex general relativity with or without a cosmological constant resembling Plebanski's action, which depends on an SO (3, C) connection, a set of 2-forms, a symmetric matrix, and a 4-form. However, it differs from the Plebanski formulation in the way that the symmetric matrix enters into the action. The advantage of this fact is twofold. First, as compared to Plebanski's action, the symmetric matrix can now be integrated out, which leads to a pure B F-type action principle for general relativity; the canonical analysis of the new action then shows that it has the same phase space of the Ashtekar formalism up to a canonical transformation induced by a topological term. Second, a particular choice of the parameters involved in the formulation produces a B F-type action principle describing conformally anti-self-dual gravity. Therefore, the new …
American Physical Society
Publication date: 
27 May 2016

Mariano Celada, Diego González, Merced Montesinos

Biblio References: 
Volume: 93 Issue: 10 Pages: 104058
Physical Review D