# What is the smallest diameter black hole that can be formed naturally?

I was watching the video I Put a 1mm Size Black Hole Next to Earth and This Happened - Universe Sandbox 2 discussing what would happen if a 1 millimeter black hole is orbiting the earth, and I began questioning myself, is it really possible to naturally have such a small black hole?

What is the smallest size that a black hole can form naturally in real life?

• Interesting question! I adjusted your wording a bit, does it still look okay?
– uhoh
Apr 11 '19 at 1:27
• sure... sorry about my poor english jejeje :V Apr 11 '19 at 1:28
• De nada, I sure wish I could speak more than one language!
– uhoh
Apr 11 '19 at 3:02
• I assume you’re excluding non-stellar black holes (eg primordial BHs) as we currently have no evidence of their existence. Since the Schwarzschild radius is derived from the mass, the starting point is the minimum stellar mass that can collapse into a black hole.... Apr 11 '19 at 7:30
• We don't know of any process that could create a 1 mm BH, apart from waiting an extremely long time so that the CMB cools down enough to let regular stellar BHs evaporate by Hawking radiation, and then waiting an insanely long time (over $10^{60}$ years) for such BHs to lose most of their mass. Apr 12 '19 at 3:34

The mass at which a star is able to condense into a black hole upon its death is called the Tolman–Oppenheimer–Volkoff Limit, which is roughly 2.17 solar masses. At this mass, the Schwarzschild radius of the black hole (the size of its event horizon) is about 6410 meters by the equation

$$r_s = \frac{2GM}{c^2}.$$

EDIT: I'd also like to add that the theoretical minimum mass for a black hole is the Planck mass, $$2.2\times 10^{−8}$$ kg, which would yield a radius of $$3.267\times 10^{-35}$$ meters, though these would not be formed by stellar collapse, though they could have formed as primordial black holes in the very early universe.

• Chandrasekhar limit is for white dwarves. Neutron stars can be >2 solar masses. Apr 19 '19 at 3:54
• nice answer! I added some links and formatted your equation using MathJax, but I wasn't sure how to parse "or 2.8 * 10^3 solar masses" properly. Feel free to edit further.
– uhoh
Apr 19 '19 at 4:21
• @MikeG I disagree, it's the upper limit at which white dwarves can be stable, and it is at this limit that collapse into a condensed body becomes possible. There is a limit, the TOV limit, which is a bit above 2 solar masses, above which "cold" neutron stars are unstable, that may be what you are thinking of? Apr 19 '19 at 15:23
• Yes. Below the TOV limit, the compact object is not a black hole. Apr 19 '19 at 16:18
• @MikeG Ok, I see what you mean now, I agree and will edit accordingly Apr 19 '19 at 17:22