Class. Quantum Grav. 37 (2020) 095010             arXiv link

BMS current algebra in the context of the Newman–Penrose formalism

Glenn Barnich¹, Pujian Mao^2,3and Romain Ruzziconi¹

1 Physique Théorique et Mathématique, Université libre de Bruxelles and International Solvay Institutes, Campus Plaine C.P. 231, B-1050 Bruxelles, Belgium

2 Center for Joint Quantum Studies and Department of Physics School of Science, Tianjin University 135 Yaguan Road, Tianjin 300350, People's Republic of China

3 Institute of High Energy Physics and Theoretical Physics Center for Science Facilities, Chinese Academy of Sciences, 19B Yuquan Road, Beijing 100049, People's Republic of China

ABSTRACT

Starting from an action principle adapted to the Newman–Penrose formalism, we provide a self-contained derivation of BMS current algebra, which includes the generalization of the Bondi mass loss formula to all BMS generators. In the spirit of the Newman–Penrose approach, infinitesimal diffeomorphisms are expressed in terms of four scalars rather than a vector field. In this framework, the on-shell closed co-dimension two forms of the linearized theory associated with Killing vectors of the background are constructed from a standard algorithm. The explicit expression for the breaking that occurs when using residual gauge transformations instead of exact Killing vectors is worked out and related to the presymplectic flux.