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May 29, 2022, 8:38:21 PMMay 29

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Let's say I start adding electrons to a black hole. As more are

added the black hole starts to develop a charge. The charge increases

as the electrons are added. At some point, will the electrons stop

being drawn into the black hole?

[[Mod. note --

As soon as the BH has any negative charge, there will be an electrostatic

repulsion between the BH and any nearby electrons. There's a limit to

how much charge you can put on a black hole and still have it be a black

hole: charged black holes always have |Q| < M in dimensionless units, i.e.,

a body with |Q| > M in dimensionless units isn't a black hole -- it's either

a solid object or it has a naked singularity at r=0.

I think (but am not quite sure) that |q|/m for electrons is large enough

that the electrostatic repulsion would be > the gravitational attraction

long before the BH charg reached |Q| = M in dimensionless units. I.e.,

I think (but am not quite sure) that the answer to your question is "yes".

See

https://en.wikipedia.org/wiki/Reissner-Nordstrom

for more on the spacetime geometry of a charged black hole.

See Misner, Thorne, and Wheeler exercise 31.8 for more on the author's

question, and for why |Q| > M isn't a black hole any more.

-- jt]]

added the black hole starts to develop a charge. The charge increases

as the electrons are added. At some point, will the electrons stop

being drawn into the black hole?

[[Mod. note --

As soon as the BH has any negative charge, there will be an electrostatic

repulsion between the BH and any nearby electrons. There's a limit to

how much charge you can put on a black hole and still have it be a black

hole: charged black holes always have |Q| < M in dimensionless units, i.e.,

a body with |Q| > M in dimensionless units isn't a black hole -- it's either

a solid object or it has a naked singularity at r=0.

I think (but am not quite sure) that |q|/m for electrons is large enough

that the electrostatic repulsion would be > the gravitational attraction

long before the BH charg reached |Q| = M in dimensionless units. I.e.,

I think (but am not quite sure) that the answer to your question is "yes".

See

https://en.wikipedia.org/wiki/Reissner-Nordstrom

for more on the spacetime geometry of a charged black hole.

See Misner, Thorne, and Wheeler exercise 31.8 for more on the author's

question, and for why |Q| > M isn't a black hole any more.

-- jt]]

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