On conserved quantities in general relativity
Abstract
Recently, definitions of total 4momentum and angular momentum of isolated gravitating systems have been introduced in terms of the asymptotic behavior of the Weyl curvature (of the underlying spacetime) at spatial infinity. Given a spacetime equipped with isometries, on the other hand, one can also construct conserved quantities using the presence of the Killing fields. Thus, for example, for stationary spacetimes, the Komar integral can be used to define the total mass, and, the asymptotic value of the twist of the Killing field, to introduce the dipole angular momentum moment. Similarly, for axisymmetric spacetimes, one can obtain the (''zcomponent'' of the) total angular momentum in terms of the Komar integral. It is shown that, in spite of their apparently distinct origin, in the presence of isometries, quantities defined at spatial infinity reduce to the ones constructed from Killing fields. This agreement reflects one of the many subtle aspects of Einstein's (vacuum) equation.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 May 1979
 DOI:
 10.1063/1.524151
 Bibcode:
 1979JMP....20..793A
 Keywords:

 04.20.Me