A single complex potential for gravity and electromagnetism

The similarity between gravity and static electricity is said to stop at the inverse square law that governs the two, and even that was disputed after the introduction of GR. Some claimed that the form of the law itself is only the result of the thinning of forces over a spherical surface that grows as the square of the radius away from the source. We show here that the similarity is in fact much more fundamental and deep because of the single origin of the two phenomenanamely EM radiation, which must be why gravity too travels at the speed of light. In [1] radiation was visualized as evaporated matter and matter as condensed radiation, since radiation carried electrical as well as mechanical attributes and when condensing in the form of a topological EM soliton, it causes the emergence of the rest of the matter attributes of mass, gravity, charge, intrinsic spin and dipole moment. The inverse square law for both gravity and electricity then appears simply as a direct consequence of momentum conservation in the condensed form [1]. This is a fundamental connection, but nonetheless it leaves one important difference. It is that similar masses attract whereas similar charges repel. However, if we took mass to be an imaginary electric charge, similar masses would repel as for electric charges and a complete similarity is achieved. With gravity fields having such imaginary values, their squares and their force effects remain real. This is then used to construct potential representations for each one of the two phenomena. The usual retarded potential integral is followed to derive a full set of fields for gravity like