Naked Science Forum

Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Richard777 on 03/02/2021 16:56:46

Title: Is there an electric equivalent to the Schwarzschild radius?
Post by: Richard777 on 03/02/2021 16:56:46

The Schwarzschild radius (r_S) is:

r_S = 2Gm/c²   

An equivalent electric radius (r_Se) may be:

r_Se = 2k_eq/c² 

Is an electric Schwarzschild mentioned in the literature?

Title: Re: Is there an electric equivalent to the Schwarzschild radius?
Post by: alancalverd on 03/02/2021 23:16:30

The equation certainly defines a length, but the interesting question is what properties are associated with that length? The notion of the radius of a massive body is fairly obvious, so we can associate distinct physical properties with objects whose physical radius r_P is greater or less than r_S but it's not immediately apparent what would happen to or around an object where r_P > r_Se or r_P < r_Se.

Would you care to put some numbers to it? The obviously interesting value of q would be one electron or proton.

Title: Re: Is there an electric equivalent to the Schwarzschild radius?
Post by: evan_au on 04/02/2021 21:26:11

It takes energy to bring like charges together.
- By the time you brought 2 solar masses of protons within a 10km diameter, you would have a conventional black hole, as a proton has pretty much the same mass as a hydrogen atom
- By mass-energy equivalence, bringing together the same number of electrons within a 10km diameter, the effective mass would be far greater than the mass of electrons alone.
            - So although the sum of the electron rest-masses would not be enough to create a black hole (by a factor of hundreds)
            - The sum of this mass and the energy to bring them together may be enough to create a black hole?
            - But it takes more time than I have available today to work out the exact limit...

This would be a charged black hole, and the charge would be visible outside the event horizon.