[Physics] Why don’t electrons collaspe into black holes?

black-holeselectrons

An electron has a mass of $9.10938291(40) \times 10^{−31} kg$. It also has a volume of $0 m^3$. This would imply it has infinite density. Shouldn't that make it collapse into a black hole? Why doesn't it?

Best Answer

The angular momentum and charge of an electron are both large enough that a black hole would not form. If you believe classical general relativity all the way down to the scale of an electron (and you really shouldn't), then the electron will form a naked singularity.

More exactly, for the case of a spinning body, the horizon is at the zero of

$$r^{2} - 2Mr + a^{2}$$

Where $a$ is the angular momentum divided by the mass (in $G = c = 1$ units), and $M$ is the black hole's mass. If you put in the numbers for the electron, this equation has no real zeroes. Adding charge to the picture will only make the matter worse.

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