Chern-Weil theorem, Lovelock Lagrangians in critical dimensions, and boundary terms in gravity actions

Nathalie Deruelle, Nelson Merino, Rodrigo Olea

Resultado de la investigación: Article

1 Cita (Scopus)

Resumen

In this paper we show how to translate into tensorial language the Chern-Weil theorem for the Lorentz symmetry, which equates the difference of the Euler densities of two manifolds to the exterior derivative of a transgression form. For doing so we need to introduce an auxiliary, hybrid manifold whose geometry we construct explicitly. This allows us to find the vector density, constructed out of spacetime quantities only, whose divergence is the exterior derivative of the transgression form. As a consequence we can show how the Einstein-Hilbert, Gauss-Bonnet and, in general, the Euler scalar densities can be written as the divergences of genuine vector densities in the critical dimensions D=2, 4, etc. As Lovelock gravity is a dimensional continuation of Euler densities, these results are of relevance for Gauss-Bonnet and, in general, Lovelock gravity. Indeed, these vectors which can be called generalized Katz vectors ensure, in particular, a well-defined variational principle with Dirichlet boundary conditions.

Idioma originalEnglish
Número de artículo044031
PublicaciónPhysical Review D
Volumen98
N.º4
DOI
EstadoPublished - 15 ago 2018

Huella dactilar

theorems
gravitation
divergence
variational principles
boundary conditions
scalars
symmetry
geometry

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)

Citar esto

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Chern-Weil theorem, Lovelock Lagrangians in critical dimensions, and boundary terms in gravity actions. / Deruelle, Nathalie; Merino, Nelson; Olea, Rodrigo.

En: Physical Review D, Vol. 98, N.º 4, 044031, 15.08.2018.

Resultado de la investigación: Article

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