# How Literal is Mass-Energy Equivalence in Gravitation?

Does, for instance, energy emit gravitational force on nearby masses, or energies, and thereby increase the overall energy of the system? (I am ignorant of field theory and would appreciate being pointed in the right direction).

If this is not true, it seems you could increase the gravitational energy between the moon and earth by converting energy to mass on earth, which is absurd as it would break the conservation of energy.

On the other hand if this is true would not the gravitational energy between the moon and earth induce additional mass-energy which then induced more gravitational force? Furthermore, which direction would this additional force be i.e. where would this added mass-energy be localized?

The electromagnetic contribution to the stress-energy tensor is simply quadratic in the field strength, e.g., the energy density being ${{T}^{00}}=\tfrac{1}{8\pi }({{E}^{2}}+{{B}^{2}})$. The divergence of this contribution to the stress-energy tensor matches the work and impulse predicted by the Lorentz force law: ${{\partial }_{\mu }}{{T}^{\mu \nu }}={{F}^{\mu \nu }}{{J}_{\mu }}$ .