Ben Rudiak-Gould

## Main Question or Discussion Point

A while ago someone asked on s.p.relativity how a black hole can accelerate

in a gravitational field, given that the round trip time to the event

horizon is infinite. This seems easy enough to understand -- given that

there's no background metric, what else could it do? But I realized that I

have no understanding of the case of a charged black hole in an external

electromagnetic field. My intuition is that it must accelerate like an

ordinary charge, and I know that there are exact solutions to GTR in which

it does just that, but I can't figure out the mechanism. Absent general

relativity, when I send an EM wave toward a point charge, I can't detect an

echoing change in its field sooner than the round-trip light travel time to

the charge. In the case of a black hole there's no charge there, at least

not in an accessible location, so how can there ever be a response? This is

making me wonder if I ever really understood general relativity.

-- Ben

in a gravitational field, given that the round trip time to the event

horizon is infinite. This seems easy enough to understand -- given that

there's no background metric, what else could it do? But I realized that I

have no understanding of the case of a charged black hole in an external

electromagnetic field. My intuition is that it must accelerate like an

ordinary charge, and I know that there are exact solutions to GTR in which

it does just that, but I can't figure out the mechanism. Absent general

relativity, when I send an EM wave toward a point charge, I can't detect an

echoing change in its field sooner than the round-trip light travel time to

the charge. In the case of a black hole there's no charge there, at least

not in an accessible location, so how can there ever be a response? This is

making me wonder if I ever really understood general relativity.

-- Ben