# Does a moving mass create a different kind of gravitational field analogous to a moving charge creating a magnetic field?

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• I’m assuming we are talking about inertial motion since you are talking about electric and magnetic fields.

As you may know, electric and magnetic fields are grouped together into the electromagnetic field tensor, Fᵤᵥ, in spacetime. What you normally think of as independent electric and magnetic field components are related in that tensor. The components are coordinate basis vector dependent meaning that different frames of reference will measure the components differently. At rest with a charge, the magnetic field components are zero.  Not at rest, they are not. But, the underlying physics is invariant but what we measure is not because we are choosing a coordinate basis for measurements.

We can make an analogy with gravity since it is also a rank 2 tensor. We derive the stress-energy tensor from 4-momentum. In special relativity, in a rest frame, the rest energy is the time component (flow) of 4-momentum. This means the corresponding stress-energy tensor has a time-time component, all others being zero.

If we are moving with respect to a gravitating source, 4-momentum gains additional relativistic components from relativistic space momentum which adds additional components to the stress energy tensor. As with the electromagnetic field tensor, we find that the components change with coordinate basis choice.

But again, the tensors represent invariant physics, but we pathetic little humans need our little coordinate basis to make our measurements so our measurements of the components of the gravitational field will change. It’s not too big of a stretch to think of curvature (gravity) being invariant, but different coordinate systems measuring the curvature in different directions as being coordinate dependent.

Of course accelerated motion can in some cases result in gravitational waves in analogy with electromagnetic waves. This is very complicated because simple acceleration of a symmetric mass will not generate gravitational waves ....

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• It's not a "different kind". It's just a gravitation field. Also, the contribution from movement and acceleration is very very tiny. Usually about 10,000,000,000 times less than the non-movement part.

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• Sort of, but not quite.

A moving mass creates gravitational waves.

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