Symmetry of gravitational field to electric field and Maxwell equation

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PBTR3
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Symmetry is an important way to find new physical laws according to Feynman. The equation that describes the electric field and the gravitational field are quite similar. Since the electric and magnetic fields are well defined by the Maxwell equations could it be possible, by symmetry, that the gravitational field has a related unknown field that could be described by a similar set of equations.

The unknown field could be dark energy or something else.

Now all I need to do is experimetally verify that that field exists.

PBTR3
 
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