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Question to the physicists out there: When an electron gets accelerated it emits "Bremsstrahlung" because it radiates away photons when it changes its velocity vector.

So for an electron on a circular path in a magnetic field, we know that it emits this radiation because this is the synchrotron radiation.

Now what happens to an electron on a circular path around a black hole? Does it emit synchrotron radiation or not?

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Bremsstrahlung radiation involves accelerating electric charges through non-zero electromagnetic fields. When all charged particles are accelerated by gravity in the same way by a [close to] uniform gravitational field then they are not being accelerated through non-zero electromagnetic fields because the causes of those fields are also accelerating in the same way. However, if an electron were falling into a charged, rotating black hole then I'd expect some Bremsstrahlung radiation indeed.

That said, IANAP. And when I say "accelerated by gravity" I am taking the interpretation that gravity is a force, which is a valid interpretation (see other commentary above).

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