Re: Throwing charges at Nordström black hole

On 1 apr, 05:35, Erik Max Francis <m...@xxxxxxxxxxx> wrote:
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 naked 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,

Towards what?

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.)

But technically, you could asymptotically approach an extremal hole,
right?

The properties of 1 solar mass Schwarzschild black hole are well
known. Its Schwarzshild radius is 1,48 km. And its gravitational
field, at larger distances, is indistinguishable from the field of an
extended object of the same mass.

What is the charge of an 1 solar mass extremal Nordström black hole?
What would be the electiric field strength at 1 a. u.?
.

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