We think that the electric field and gravitational field operate similarly with their corresponding charges/masses. With just a difference that the electric field is sometimes attractive and sometimes repulsive.
Now I have read that when a charged particle moves the electric field lines associated with it, it is distorted in one way because of the finite time required to get propagated, and this is the cause of the existence of the magnetic field (if calculus is used it can be proven mathematically).
So why is it not the same with the gravitational field? Why is there nothing like a Gravitational Magnetic Field?