### 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 original | English |
---|---|

Número de artículo | 044031 |

Publicación | Physical Review D |

Volumen | 98 |

N.º | 4 |

DOI | |

Estado | Published - 15 ago 2018 |

### Huella dactilar

### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

### Citar esto

*Physical Review D*,

*98*(4), [044031]. https://doi.org/10.1103/PhysRevD.98.044031

}

*Physical Review D*, vol. 98, n.º 4, 044031. https://doi.org/10.1103/PhysRevD.98.044031

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

Resultado de la investigación: Article

TY - JOUR

T1 - Chern-Weil theorem, Lovelock Lagrangians in critical dimensions, and boundary terms in gravity actions

AU - Deruelle, Nathalie

AU - Merino, Nelson

AU - Olea, Rodrigo

PY - 2018/8/15

Y1 - 2018/8/15

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85052651764&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.98.044031

DO - 10.1103/PhysRevD.98.044031

M3 - Article

VL - 98

JO - Physical Review D

JF - Physical Review D

SN - 2470-0010

IS - 4

M1 - 044031

ER -