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a steadily rotating electric charge current causes a magnetostatic field

A steadily rotating mass must cause a gravitomagnetostatic field.

Electrostatic field of an electric monopole charge is a potential field. Its integral through any closed circuit is zero.

A gravitostatic field of a mass monopole charge is also a potential field. Its integral through any closed circuit is also zero.

When a magnetic field varies in time, it causes electromotive field. It is electric field, but it is allowed to have nonzero integral through closed circuits.

What happens when gravitomagnetic field varies through time, for example due to orbital movement?

Can varying gravitomagnetic field include a gravitomotive field, with nonzero integral over closed circuits?

In other words, can varying gravitomagnetic field cause a wheel to rotate?