I know that general relativity unifies the electric charge with the magnetic field via relative motion. So if I accelerate a charge then anyone in another inertial frame will see a magnetic field. Einstein also tells us that the effects of acceleration are indistinguishable from the effects of gravity. Does this mean that a charge in a gravitational field will likewise be seen as a magnetic field?
The answer is no if the gravitational field is static. I'm not sure what will happen if the field is not static.
Let me quote a paragraph from Wolfgang Rindler's Relativity - Special, General, and Cosmological (2nd edition, ISBN 44198567324), Sec.1.15 (P.22-23):
Consider the following notorious paradox: an electric charge is at rest on the surface of the earth. By conservation of energy (or just by common sense!), it will not radiate. And yet, relative to an imagined freely falling cabin around it, that charge is accelerating. But charges that accelerate relative to an IF radiate. Why doesn’t ours? Again, consider a charge that is fixed inside an earth-orbiting space capsule. Now, circularly moving charges do radiate, and one cannot imagine how the earth’s gravitational field could change that. But relative to the freely falling space capsule the charge is at rest, and charges at rest in an inertial frame do not radiate. Where is the catch? Much has been written on these paradoxes, but the proper solution seems to have been first recognized by Ehlers: It is necessary to restrict the class of experiments covered by the EP to those that are isolated from bodies or fields outside the cabin. In the case of the charges discussed above, their electric field extends beyond the cabin and is, in fact, ‘anchored’ outside; since radiation is a property of that whole field, it follows that these ‘experiments’ lie outside the scope of the EP.
In the above case, we can see that not all effects of acceleration are indistinguishable from the effects of gravity.
Another example is that gravitational field felt by an object may be non-uniform (e.g. gravitational attraction from the Earth felt by a satellite), while acceleration does not.