A note on dual gravitational charges

TL;DR

This paper investigates the origin and properties of dual gravitational charges, showing they stem from an exact 3-form in tetrad variables and analyzing their behavior under different symmetries using covariant phase space and cohomological methods.

Contribution

It reveals the origin of dual gravitational charges from tetrad variables and clarifies their behavior under various symmetries using covariant phase space and Barnich-Brandt methods.

Findings

Dual charges originate from an exact 3-form in tetrad variables.

Dual charges vanish for exact isometries and at spatial infinity.

Dual charges persist at future null infinity for asymptotic symmetries.

Abstract

Dual gravitational charges have been recently computed from the Holst term in tetrad variables using covariant phase space methods. We highlight that they originate from an exact 3-form in the tetrad symplectic potential that has no analogue in metric variables. Hence there exists a choice of the tetrad symplectic potential that sets the dual charges to zero. This observation relies on the ambiguity of the covariant phase space methods. To shed more light on the dual contributions, we use the Kosmann variation to compute (quasi-local) Hamiltonian charges for arbitrary diffeomorphisms. We obtain a formula that illustrates comprehensively why the dual contribution to the Hamiltonian charges: (i) vanishes for exact isometries and asymptotic symmetries at spatial infinity; (ii) persists for asymptotic symmetries at future null infinity, in addition to the usual BMS contribution. Finally, we point out that dual gravitational charges can be equally derived using the Barnich-Brandt prescription based on cohomological methods, and that the same considerations on asymptotic symmetries apply.