Kinetic energy effect on spacetime Given an electric field E in space. The electric field has an energy density associated with it, which does curve spacetime. When the electric field does work on a charge it loses the same amount of energy as the charge gains from KE (+ any em wave production).
Does the kinetic energy that the charge has, effect spacetime the same way as if it were still in the electric field?
My initial thought was YES. However, if I now switch frames to the moving charge it has 0 kinetic energy and therefore would obviously not effect spacetime. How can this energy effect spacetime if its in the EM field, but not if converted to KE.
Obviously some of my assumptions are wrong. Can anyone help?
 A: The source of gravity is not just energy, but rather the stress energy tensor. Energy density is just one component of the tensor, and the other components include momentum density, pressure, and shear stress. It is important to keep in mind not just the energy density but also the effects on the rest of the stress energy tensor components.
For a given stress energy tensor it does not matter if the stress energy is in the form of an EM field or in the form of matter. Of course, there is more flexibility in matter, so there will be some configurations of matter that have a stress energy tensor that cannot be duplicated by the EM field. But regardless, there is no distinction between the type of source in terms of how its stress energy gravitates.
Regarding your question about the particle and it’s energy in multiple frames. You are correct that in some frames it has more kinetic energy than in others. However, that is not the only change, it also has more momentum than in other frames. As you decrease the energy component you also decrease one of the momentum components. The combination of reducing both the energy and the momentum component is to make the gravitational field simply be the expected transformation of the original gravitational field.
