1995/04/28 by J. N. Goldberg, J N Goldberg, C. Soteriou +1 · 23 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Einstein #Gauge theory #General relativity #Gravitation #Gravitational field #Minkowski space #Null (SQL) #Phase space #Pulsars and Gravitational Waves Research #Space time #Spacetime #gr-qc
paper · pdf · doi:10.1088/0264-9381/12/11/010
published in Classical and Quantum Gravity 12(11), 2779-2797 (IOP Publishing) · magnification set; pagination improved; 20 pages, plain tex
arxiv created 1995/04/28 · openalex publication_date 1995/11/01 · arxiv updated 2010/11/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We use the canonical formalism developed together with David Robinson to study the Einstein equations on a null surface. Coordinate and gauge conditions are introduced to fix the triad and the coordinates on the null surface. Together with the previously found constraints, these form a sufficient number of second-class constraints so that the phase space is reduced to one pair of canonically conjugate variables: and . The formalism is related to both the Bondi - Sachs and the Newman - Penrose methods of studying the gravitational field at null infinity. Asymptotic solutions in the vicinity of null infinity which exclude logarithmic behaviour require the connection to fall off like after the Minkowski limit. This, of course, gives the previous results of Bondi - Sachs and Newman - Penrose. Introducing terms which fall off more slowly leads to logarithmic behaviour which leaves null infinity intact, allows for meaningful gravitational radiation, but the peeling theorem does not extend to in the terminology of Newman - Penrose. The conclusions are in agreement with those of Chrusciel, MacCallum and Singleton. This work was begun as a preliminary study of a reduced phase space for quantization of general relativity.