I've been wondering if it's possible for a black hole to interfere with the electromagnetic field of an electric charge, without the black hole itself having an electric charge.
Imagine that there is a Schwarszchild black hole somewhere and far away, an electric charge. This electric charge will generate an electric field that, given enough time, will spread throughout the universe. At some point this electric field will encounter the black hole which is capable of drastically distorting the space-time around it.
Around the black hole, the electric field lines are no longer radial as they are close to the charge that generates them, there are even lines that are interrupted by it (the lines that fall radially into the black hole).
I imagine that, therefore, even though it has no electrical charge, the black hole is interacting with the electromagnetic field. So far so good, but what happens if this black hole accelerates in some direction or starts to rotate?
If it does this, the electric field lines of the electric charge will start to change direction, as would happen near the electric charge if the electric charge itself were accelerating.
If it were the case of the electric charge itself accelerating, we would conclude that this charge would be generating electromagnetic waves (light) due to the acceleration.
Now, if the black hole accelerates, will it generate electromagnetic waves in this electromagnetic field that it is not producing?
If so, it means a black hole can generate eletromagnetic waves in a third body's eletromagnetic field even though it does not have charge itself?
The problem is that if there is radiation being generated, there is energy being released. Where would that energy come from in this case? From the black hole or from the electric charge? It would be like a "classical" Hawking radiation?