Hamiltonian derivation of dual gravitational charges

TL;DR

The paper provides a Hamiltonian derivation of dual BMS gravitational charges within a first-order Palatini-Holst framework, showing the Holst term (or Nieh-Yan term with torsion) is responsible for dual charges despite not altering Einstein equations. Using the covariant phase space formalism and Wald-Zoupas prescription, the authors extract the leading integrable dual charges and establish their algebra, including a field-dependent central extension. They demonstrate the standard BMS charges arise from the Palatini part while dual charges arise from the Holst term, and show Lorentz charges are trivial under their boundary conditions. The analysis is extended to include fermions, where Nieh-Yan terms ensure dual charges remain well-defined in torsionful spacetimes, tying the results to Newman-Penrose charges and outlining directions for subleading charges and alternative formalisms.

Abstract

We provide a Hamiltonian derivation of recently discovered dual BMS charges. In order to do so, we work in the first order formalism and add to the usual Palatini action, the Holst term, which does not contribute to the equations of motion. We give a method for finding the leading order integrable dual charges à la Wald-Zoupas and construct the corresponding charge algebra. We argue that in the presence of fermions, the relevant term that leads to dual charges is the topological Nieh-Yan term.