[Richard777 (OP)]

If; the vector operator (DeL) transforms to a scalar operator,
Then;   
divergence may transform to a dot product
curl may transform to a cross product

The Maxwell equations include four laws, two divergence laws and two curl laws. The four laws are;
The Gauss Law,
the Magnetic Law,
the Faraday Law,
the Ampere Law.

These laws may be re-written for gravity. Gravitoelectromagnetism (GEM) compares the “Maxwell field equations” for electromagnetism with similar field equations for gravity. This comparison includes “gravitational magnetism” (gravitomagnetism) which is the assumed distortion of a gravitational field due to the motion of a massive object. Mass is analogous to charge.

If DeL does transform, then the Maxwell Equations for gravity may transform as follows;
The Gauss Law transforms to the acceleration rule
The Magnetic Law transforms to the size rule
The Faraday Law transforms to the force rule
The Ampere Law transforms to the power rule.

Will a scalar transformation of Del and GEM give equivalent scalar rules?