How does black hole entropy relate to horizon area for moving observers?

[touqra]

If the entropy, S of a black hole is proportional to the area of the horizon, A, then, what about an observer moving with a constant velocity, v with the BH? Another observer moving with a constant acceleration with respect to the BH?
After all, entropy is an invariant but area is not. So, isn't this a problem?

 

[mccrone]

Unruh radiation?