Hello,(adsbygoogle = window.adsbygoogle || []).push({});

I've been quite avidly reading about one of the spectacular recent joint achievements of physics and pure math. The positive energy theorem [1,2,3] concerns the large-distance asymptotic behaviour of the gravitational field due to a localised distribution of mass-energy. I think I paraphrase the theorem correctly to say that, provided the source is physical (energy density T_00 is everywhere positive in every local Lorentz frame), then the energy of the system, as inferred from the large-distance gravitational field, is also positive. A neat and powerful result.

I was wondering if a similar result holds for electromagnetic theory. If we take Maxwell's equations and again impose that the source is physical (the current J_\mu is future-timelike), does this place some analogous constraint on the large-distance behaviour of the associated electromagnetic field? This linear system should presumably be much easier than the hard-core nonlinearity of Einstein GR, but nothing obvious jumped out at me.

Thanks,

Dave

* [1] Schoen, R. and Yau, S-T., Commun. Math. Phys, 65 (1979) 45

* [2] Witten, E., Commun. Math. Phys. 80 (1981) 381

* [3] Kazdan, J., Seminaire N. Bourbaki, 24 (1982) 315, Exp 593

[3], a review article, is publicly available at http://www.numdam.org/numdam-bin/browse?j=SB [Broken]

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Electromagnetic version of the positive energy theorem?

**Physics Forums | Science Articles, Homework Help, Discussion**