Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 16 (2020), 046, 50 pages      arXiv:1909.10088      https://doi.org/10.3842/SIGMA.2020.046

Routh Reduction of Palatini Gravity in Vacuum

Santiago Capriotti
Departamento de Matemática, Instituto de Matemática de Bahía Blanca (INMABB), CONICET, Universidad Nacional del Sur, Av. Alem 1253, 8000 Bahía Blanca, Argentina

Received September 24, 2019, in final form May 11, 2020; Published online May 30, 2020

Abstract
An interpretation of Einstein-Hilbert gravity equations as Lagrangian reduction of Palatini gravity is made. The main technique involved in this task consists in representing the equations of motion as a set of differential forms on a suitable bundle. In this setting Einstein-Hilbert gravity can be considered as a kind of Routh reduction of the underlying field theory for Palatini gravity. As a byproduct of this approach, a novel set of conditions for the existence of a vielbein for a given metric is found.

Key words: symmetry reduction; Palatini gravity; frame bundle.

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