On the general definition of angular momentum in general relativity and the axial symmetric case

EMANUEL GALLO; O. M. MORESCHI

Villa General Belgrano

Conferencia; GRAV13; 2013

IFEG-CONICET y FaMAF-UNC

The subject of the appropriate notion of angular momentum in general relativity is a difficult one and has been tackled by numerous authors. Although there are many works in the subject, different approaches have yielded nonequivalent definitions; most of them suffering from the so called supertranslations ambiguities. One of the main reasons why it is so difficult to define angular momentum at null infinity comes from the fact that the asymptotic symmetries group is not the 10-dimensional Poincare group, but the infinite dimensional BMS group. And this larger group gives origin to the problem of supertranslations. In the past, one of the authors was able to provide a definition of intrinsic angular momentum based on charge integrals of the Riemman tensor, which have circumvented those problems and provided at the same time with the notion of center of mass at future null infinity. However in this work no conclusive relation with the Komar integral was stated, for the case of rotational symmetry. In this work we would like to improve on this situation. After a review of the general problem, we introduce and analyze here the most general notion of intrinsic angular momentum based on charge integrals; which is valid for general asymptotically flat spacetimes, and is free from supertranslations ambiguities, and reduces to the Komar integral in the case of axial symmetry.