只要提供一個合適的演化向量和適當的背景幾何，哈氏量的邊界項能給出引力場準局 域的值。本文的目標在建構一套最佳化的辦法來確定適當的背景值。首先將封閉二維面 上度規的十個分量，從動力學時空等度規地嵌入到在背景幾何上， 然後透過要求準局域 能量取極值的方法來確定適當的背景值。這套辦法也同時決定了演化向量的選取。我們 以軸對稱的動力學時空，針對克爾度規的情況明確地計算了準局域的能量和角動量。 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 geometry. On the two-surface boundary of a region we have proposed using 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.
