Rigorous Formulation of Duality in Gravitational Theories

Details Rigorous Formulation of Duality in Gravitational Theories Rigorous Formulation of Duality in Gravitational Theories

2009-10-11

arxiv.org/abs/0910.2021v1

J. Phys. A: Math. Theor. 43 (2010) 205206

Physics

Mathematical Physics

15 pages

Scientific paper

10.1088/1751-8113/43/20/205206

In this paper we evince a rigorous formulation of duality in gravitational theories where an Einstein like equation is valid, by providing the conditions under which the Hodge duals (with respect to the metric tensor g) of T^a and R_b^a may be considered as the torsion and curvature 2-forms associated with a connection D', part of a Riemann-Cartan structure (M,g',D'), in the cases g = g' and g does not equal g', once T^a and R_b^a are the torsion and curvature 2-forms associated with a connection D part of a Riemann-Cartan structure (M,g,D). A new form for the Einstein equation involving the dual of the Riemann tensor of D is also provided, and the result is compared with others appearing in the literature.

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