Null asymptotics of solutions of the EinsteinMaxwell equations in general relativity and gravitational radiation

Lydia Bieri PoNing Chen Shing-Tung Yau

Mathematical Physics mathscidoc:1912.43578

Advances in Theoretical and Mathematical Physics, 15, (4), 1085-1113, 2011
We prove that for spacetimes solving the EinsteinMaxwell (EM) equations, the electromagnetic field contributes at highest order to the nonlinear memory effect of gravitational waves. In Nonlinear nature of gravitation and gravitational-wave experiments, Christodoulou showed that gravitational waves have a nonlinear memory. He discussed how this effect can be measured as a permanent displacement of test masses in a laser interferometer gravitational-wave detector. Christodoulou derived a precise formula for this permanent displacement in the Einstein vacuum (EV) case. We prove in Theorem 2.6 that for the EM equations this permanent displacement exhibits a term coming from the electromagnetic field. This term is at the same highest order as the purely gravitational term that governs the EV situation. On the other hand, in Section 3, we show that to leading order, the presence of the electromagnetic field
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@inproceedings{lydia2011null,
  title={Null asymptotics of solutions of the EinsteinMaxwell equations in general relativity and gravitational radiation},
  author={Lydia Bieri, PoNing Chen, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204205078440142},
  booktitle={Advances in Theoretical and Mathematical Physics},
  volume={15},
  number={4},
  pages={1085-1113},
  year={2011},
}
Lydia Bieri, PoNing Chen, and Shing-Tung Yau. Null asymptotics of solutions of the EinsteinMaxwell equations in general relativity and gravitational radiation. 2011. Vol. 15. In Advances in Theoretical and Mathematical Physics. pp.1085-1113. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204205078440142.
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