Open Access
April 2006 On the relation between ADM and Bondi energy--momenta
Xiao Zhang
Adv. Theor. Math. Phys. 10(2): 261-282 (April 2006).


When a spacetime takes Bondi radiating metric and is vacuum and asymptotically flat at spatial infinity which ensures the positive mass theorem, we prove that the standard ADM energy--momentum is the past limit of the Bondi energy--momentum. We also derive a formula relating the ADM energy--momentum of any asymptotically flat spacelike hypersurface to the Bondi energy--momentum of any null hypersurface. The formula indicates that the Bondi mass is always less than the ADM total energy if the system has news. The assumed asymptotic flatness precludes gravitational radiation. We therefore study further the relation between the ADM total energy and the Bondi mass when gravitational radiation emits. We find that, in this case, the ADM total energy is no longer the past limit of the Bondi mass. They differ by certain quantity relating to the news of the system.


Download Citation

Xiao Zhang. "On the relation between ADM and Bondi energy--momenta." Adv. Theor. Math. Phys. 10 (2) 261 - 282, April 2006.


Published: April 2006
First available in Project Euclid: 30 July 2006

zbMATH: 1157.83321
MathSciNet: MR2249573

Rights: Copyright © 2006 International Press of Boston

Vol.10 • No. 2 • April 2006
Back to Top