# Field-theoretical construction of currents and superpotentials in Lovelock gravity

## TL;DR

This paper develops a comprehensive, exact field-theoretical framework for constructing conserved currents and superpotentials in Lovelock gravity, applicable to arbitrary backgrounds and perturbations, including black hole solutions.

## Contribution

It introduces a novel, exact method based on Noether identities for deriving conserved quantities in Lovelock gravity, extending previous approaches.

## Key findings

- Constructed conserved currents and superpotentials for Lovelock gravity.
- Applied the formalism to compute the mass of Schwarzschild-AdS black holes.
- Compared the new method with the Abbott-Deser-Tekin approach.

## 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 $D$ dimensions. Proposals for future applications are presented.