# Charged black hole in electromagnetic field

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

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CarlB
Ben Rudiak-Gould wrote:
> 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.

I wonder if Lasenby Doran and Gull's elegant analysis of black holes
and electric charges will give a better intuitive understanding of this
problem
than the usual GR formulation:

http://xxx.lanl.gov/abs/gr-qc/0405033

In particular, see Figure 5, page 85, for the field lines between a
point
charge around (and in) a nearby black hole. (The link is to the
updated
version of their 1998 paper.)

Jonathan Scott
The electrostatic field of the charge must have been present in the
surrounding space since the time the charge was introduced into the
vicinity of the black hole (or of the progenitor body), so there's no
need to get near the charge to know that it's there or interact with
its field. However, I'd also be interested in a good answer to this
question.

Chris Hillman
Some recent FAQs, fads, and fallacies at s.p.r.

The electrostatic field of the charge must have been present in the surrounding space since the time the charge was introduced into the
vicinity of the black hole (or of the progenitor body), so there's no
need to get near the charge to know that it's there or interact with
its field. However, I'd also be interested in a good answer to this
question.
In fact, Jonathan has answered the question. This is in fact a (minor and very common variant of a) FAQ; see http://www.math.ucr.edu/home/baez/physics/Relativity/BlackHoles/black_gravity.html and "How does Gravity Escape from a Black Hole?" at http://www.math.ucr.edu/home/baez/RelWWW/group.html [Broken]

I wish to avoid debunking, but sadly note that several recent s.p.r. posts (not from physicists!) have credulously promoted some awfully cranky notions, but have been met with little or no critical response.

Let me just briefly mention two general concerns.

In my view, scientists and indeed all citizens should be gravely concerned by the deplorable spectacle of attorneys (and elected officials) acting on behalf of for-profit companies (which in fact seem to subsist soley on investment monies, since their supposed devices contravene generally accepted principles of physics and thus, not suprisingly, apparently don't work) attempting to interfere with the standard checks and balances of the scientific process by intimidation and harrassment of authors of critical comments/reports.

A second grave concern involves evidence of systematic campaigns by certain such companies to attract further investment by manipulation of various media, such as newspapers, UseNet newsgroups, and other web forums such as the Wikipedia, into presenting slanted information, misinformation, or disinformation aimed at attracting investment in scientifically dubious "fringe physics" schemes for power generation and the like. In the most notorious cases, a few such companies have apparently made considerable progress toward their goal of being generously funded by various governments (U.S. and Europe), which in my view should be cause for particular concern. My point is that our global energy situation is serious and it makes sense to focus on research which has a realistic chance of ameliorating this situation sometime in the foreseeable future.

'Nuff said (at least by myself): if you want to know more, Google.

Last edited by a moderator:
Bill J.
Ben Rudiak-Gould wrote:
> 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

How about an example to get things started:

Put the charged black hole in between the plates of an idealized really
huge parallel-plate capacitor with initial charge 0.

Now charge the capacitor to a finite voltage V through a resistor to
keep from getting spurious infinities from instantly letting the field
jump up from 0.

What then happens to the observed position of the black hole from the
point of view of an observer at rest with respect to the capacitor?