10 Exact Gravitationally-Conserved Quantities

✍ Scribed by Newman, E. T.; Penrose, R.

• Book ID: 120827594
• Publisher: The American Physical Society
• Year: 1965
• Tongue: English
• Weight: 178 KB
• Volume: 15
• Category: Article
• ISSN: 0031-9007
• DOI: 10.1103/PhysRevLett.15.231

✦ Synopsis

In ordinary electromagnetic theory, total charge remains exactly constant for any system surrounded by source-free space. This is a direct consequence of Maxwell's equations for the free-space region, whereas dipole and higher moments can be carried away by electromagnetic radiation. In gravitational theory, analogs of this conserved charge would, at first sight, appear to be mass, momentum, and an- gular momentum, as they are indeed exactly conserved in the linearized Einstein theory, for regions surrounded by empty space. ~' However, in the full nonlinear theory mass and momentum can be changed (i.e. , "carried away") by gravitational radiation. 5 It has therefore been commonly believed that there are no (nontrivial) exactly conserved (covari- ant) gravitational quantities in general relativity. But it turns out that, quite unexpectedly,