General Relativity and Gravitation

, Volume 45, Issue 3, pp 545–579 | Cite as

Covariantized Nœther identities and conservation laws for perturbations in metric theories of gravity

Research Article

Abstract

A construction of conservation laws and conserved quantities for perturbations in arbitrary metric theories of gravity is developed. In an arbitrary field theory, with the use of incorporating an auxiliary metric into the initial Lagrangian covariantized Nœther identities are carried out. Identically conserved currents with corresponding superpotentials are united into a family. Such a generalized formalism of the covariantized identities gives a natural basis for constructing conserved quantities for perturbations. A new family of conserved currents and correspondent superpotentials for perturbations on arbitrary curved backgrounds in metric theories is suggested. The conserved quantities are both of pure canonical Nœther and of Belinfante corrected types. To test the results each of the superpotentials of the family is applied to calculate the mass of the Schwarzschild-anti-de Sitter black hole in the Einstein–Gauss–Bonnet gravity. Using all the superpotentials of the family gives the standard accepted mass.

Keywords

Metric gravitation theories Differential identities Conservation laws 

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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Sternberg Astronomical InstituteMoscow MV Lomonosov State UniversityMoscowRussia
  2. 2.Department of PhysicsUzhgorod National UniversityUzhgorodUkraine

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