Crown-Horned Snorkack wrote:
> Suppose you have a Nordström black hole.
It's Reissner-Nordström, by the way.
> At large distance, both Newton gravitational attraction and Coulomb
> repulsion increase with inverse square of distance. Therefore, you can
> pick test bodies with suitable mass to charge ratio that the Coulomb
> repulsion exactly compensates Newton attraction irrespective of
> distance. The charge would not feel the presence of black hole.
>
> What about close to black hole? Does a small test body with like
> charge to Nordström black hole still feel infinite attraction at even
> horizon and large but finite attraction outside and near the horizon?
We've already covered these cases in past questions. With a normal,
stable black hole of any type, the event horizon presents a boundary
through which one can never escape. It depends on the properties (mass,
angular momentum, charge) of the black hole, not of objects falling
near/into it. Inside the event horizon, the radial coordinate turns
timelike and to move forward in time is to move closer to the
singularity and one's inevitable destruction. In general relativity,
gravity isn't simply a force; it's part of the structure of spacetime.
And inside such an event horizon,
> What about a Nordström black hole and test bodies such that the
> Coulomb repulsion exceeds the Newton attraction for all large
> distances? Does the infinite attraction at event horizon still apply?
> And would there also be large but finite attraction outside and near
> event horizon? As well as large but finite Coulomb repulsion somewhere
> outside?
The special cases are for extreme Reissner-Nordström black holes, and
beyond-extreme holes. The beyond-extreme holes have ****d singularities
and aren't thought to be physical (especially since the enormous
charge-to-mass ratio that would be required which would make them
basically impossible). The extreme case is interesting but is also
thought to be academic; there, the inner and outer event horizons meet
together to make a single event horizon, but curiously, the radial
coordinate does not become timelike inside it; it remains spacelike. So
you can enter the event horizon and exit out of it again ... but you
exit out of it in another universe.
However, since extremal black holes require charge and mass ratios that
are perfectly balanced (and enormous), they are unstable, and thus not
thought to represent anything physically possible.
> Can you throw charges at Nordström black hole, which are repelled by
> Coulomb repulsion but cross the barrier by their kinetic energy and
> add to the charge of the hole?
Sure, if you throw it hard enough to overcome Coulomb repulsion.
> How far can that process go?
I do not believe you can make a non-extremal Reissner-Nordström into an
extreme one by adding charge, though I might be mixing that up with Kerr
black holes and adding angular momentum. (I think they're all part of
the same case with Kerr-Newman holes, though.)
--
Erik Max Francis && max@[EMAIL PROTECTED]
&& http://www.alcyone.com/max/
San Jose, CA, USA && 37 18 N 121 57 W && AIM, Y!M erikmaxfrancis
Man is a clever animal who behaves like an imbecile.
-- Albert Schweitzer
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