Which rule determines the direction of gravitomagnetism?

[adm2e]

Do you use a left-hand or right-hand rule with gravitomagnetism?

 

[pervect]

Usually people use a tensor formulation for the combined gravitoelectric and gravitomagnetic field, similar to the way that the Faraday tensor for electromagnetism combines the electric field and the magnetic field.

See http://en.wikipedia.org/w/index.php?title=Electromagnetic_tensor&oldid=150939457

for a discussion of the Faraday tensor.

However, I suppose you could represent the gravitomagnetic field as a vector, as long as you don't try and transform it as a vector (the same caution applies to the tensor form - it "looks like" a tensor, but it doesn't transform as one).

If you did chose to represent it via a vector, I'd recommend using the right hand rule.