## An Optimal Choice of Reference for the Quasi-Local Gravitational Energy and Angular Momentum    [PDF]

Gang Sun, Chiang-Mei Chen, Jian-Liang Liu, James M. Nester
The boundary term of the gravitational Hamiltonian can be used to give the values of the quasi-local quantities as long as one can provide a suitable evolution vector field and an appropriate reference. On the two-surface boundary of a region we have proposed using {\em four dimensional isometric matching} between the dynamic spacetime and the reference geometry along with energy extremization to find both the optimal reference matching and the appropriate quasi-Killing vectors. Here we consider the axisymmetric spacetime case. For the Kerr metric in particular we can explicitly solve the equations to find the best matched reference and quasi-Killing vectors. This leads to the exact expression for the quasi-local boundary term and the values of our optimal quasi-local energy and angular momentum.
View original: http://arxiv.org/abs/1307.1039