Null boundary gravitational charges from local Lorentz symmetries

TL;DR

This paper explores null boundary gravitational charges, revealing that trivial terms like the Holst term can generate new boundary degrees of freedom through local Lorentz symmetries.

Contribution

It uncovers a new gravitational charge from the Holst term, highlighting the role of trivial terms in boundary degrees of freedom.

Findings

Discovered an additional charge from local Lorentz transformations.

Showed trivial terms can influence boundary degrees of freedom.

Highlighted the significance of the Holst term in boundary charge analysis.

Abstract

In this paper, we revisit the null boundary gravitational charge in the Newman-Penrose formalism with special emphasis on the charges from local Lorentz transformations. We find that there is one more charge derived from the local Lorentz transformation and the new charge is purely from the Holst term. This reveals a remarkable fact that trivial terms which do not change classical equations of motion can not only affect the boundary degrees of freedom through their contributions to the boundary charges but also have their own rights to create new boundary degrees of freedom.