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Newton's law of gravity is ∇.(∇Φ) = 4πGρ.

A book on GR gives a suggestion to make it Lorentz covariant by using de' Alembertian operator on 'Φ' in the LHS of above equation instead of Laplacian. Then it explains that this won't work because we have to include in 'ρ' all the energy density also in addition to mass density since mass and energy are equivalent according to Special Relativity. I am not able to understand the logic behind this. Mass may be equivalent to energy but the gravitational potential should result only from the mass. I mean if I have some energy in the form of electric field, why should I include this electric energy density in 'ρ' to obtain gravitational potential?

Thank you!

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# Covariant form of Newton's law of gravity

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