Field-theoretical construction of currents and superpotentials in Lovelock gravity
arXiv:1903.05500 · doi:10.1088/1361-6382/ab516d
Abstract
Conserved currents and related superpotentials for perturbations on arbitrary backgrounds in the Lovelock theory are constructed. We use the Lagrangian based field-theoretical method where perturbations are considered as dynamical fields propagating on a given background. Such a formulation is exact (not approximate) and equivalent to the theory in the original metric form. From the very start, using Noether theorem, we derive the Noether-Klein identities and adopt them for the purposes of the current work. Applying these identities in the framework of Lovelock theory, we construct conserved currents, energy-momentum tensors out of them, and related superpotentials with arbitrary displacement vectors, not restricting to Killing vectors. A comparison with the well known Abbott-Deser-Tekin approach is given. The developed general formalism is applied to give conserved quantities for perturbations on anti-de Sitter (AdS) backgrounds. As a test we calculate mass of the Schwarzschild-AdS black hole in the Lovelock theory in arbitrary dimensions. Proposals for future applications are presented.
29 pages, to appear in Class. Quantum Grav
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- Black holes of the Vaidya type with flat and (A)dS asymptotics as point particles
- Conserved quantities for black hole solutions in pure Lovelock gravity