# Minimum size of black hole

What is the minimum size a black hole could be? I have been told that they were worried that the LHC would create a black hole, yet they say the Sun cannot be a black hole. I understand that the black hole may evaporate very quickly, but I still don't understand what the minimum size is.

• Duplicate of How small are the smallest black holes?. Apr 10, 2015 at 22:10
• @ACuriousMind and Jimmy360 I do mean any black hole. Not just stable black holes. Apr 10, 2015 at 22:18
• It's not that the Sun "cannot" be a black hole, it's that the process that makes a star into a black hole won't work unless there's enough mass. There has to be so much gravity that nothing can stop the collapse. Less mass and something--electron degeneracy pressure for white dwarves, etc--will be able to make it balance. Apr 10, 2015 at 22:19
• Then I don't think there is any such limit - in classical GR, if you get the required mass inside the Schwarzschild radius, you get a black hole. In reality, there will probably quantum effects at very small scales making that classical statement invalid, but since we do not have a quantum theory of gravity, there can't be an accepted answer what happens. Apr 10, 2015 at 22:20

There's no minimum size. There's a minimum density. Stars turn themselves into black holes when they exhaust their fuel and collapse. For that to yield a black hole, they need to start off with around 25 solar masses. If a star starts with enough mass, natural processes cause it to eventually suffer a core collapse which greatly compresses some of its mass. (The rest gets blasted outward into space by the resulting shockwave.) If that explosion's large enough, the mass that's falls inward can reach the critical density for a black hole. (Thus the black hole's mass is less than that of the progenitor star.)

Particle accelerators can (perhaps, according to some versions of theory) create microscopic black holes by manufacturing large subatomic particles. Since the particles are created with high nominal densities, they can be considered black holes. They also tend to be moving near the speed of light, and even though they're "large subatomic particles", they're still expected to have masses much less than, say, a Uranium atom. Since it's the total mass which sets a black hole's radius, this would yield (at worst) nucleus-scale black holes moving near the speed of light. Such black holes would drill through matter, disrupting anything encountered along the way in a nucleus-wide path. Since atoms are really small (and nuclei are even smaller), you could have a few of these going through you and not notice... but they'd technically be black holes. The "disruption" caused by them would basically be a narrow beam of ionizing radiation. Such black holes would also decay very rapidly.

• I thought the density of the center of all black holes is infinity because a singularity has infinite density and zero volume. Apr 10, 2015 at 22:27
• Massive stars do not explode due to thermonuclear runaway, that is the low-mass stars. Massive stars go through core-collapse. And you typically need at least 25 solar masses to get a black hole. Apr 10, 2015 at 22:32
• Thanks to @kyle-kanos for correcting me. To answer benichiwa's concern: The singularity itself reaches possibly-infinite density, but there's a convention of referring to the size of a black hole based on the radius of the event horizon. The black hole's mass can be divided by that volume to yield the density I intended above. My original answer is probably still fudging things slightly, but if Kyle or another astrophysicist can come up with a more-accurate concise answer, I invite them to do so. Apr 13, 2015 at 21:06
• This scenario (I mean paragraph 2) sounds quite wrong to me. What about Hawking radiation? To get to the moon, travelling at the speed of light, you would have to create black holes of mass $>10^{5}$ kg, since a lower mass black hole would evaporate in a fraction of a second, releasing $\sim 10^{21}$ J during that time. The black holes you are talking about would evaporate in a vanishingly short time. Apr 13, 2015 at 22:04
• I did ignore Hawking radiation, and didn't mean to treat the LHC as a shoot-down-the-Moon gun. I was trying to show that the black-holes one might get from the LHC would not stick around long enough for the Earth to get sucked in. Such was a concern in some quarters before the accelerator's upgrade. I'll remove the lunar sentence. Apr 14, 2015 at 22:08

I agree with the previous answers which say that within classical GR there is no such thing as minimal BH size. However, there might be a limit if quantum effects are taken into account. In the absence of consistent theory of quantum gravity, it does not go beyond mere hypothesizing, but there are some conjectures which you are free to embrace or discard. Take this paper by J. Bekenstein as an example arXiv: gr-qc/9710076. In short, Bekenstein conjectures that the horizon area of a black hole can be thought of as an adiabatic invariant of a black hole which, according to the prescriptions of the old quantum theory, needs to be quantized. The size of area quantum turns out to be on the order of [Planck length]$$^2$$, which gives you the minimum BH radius.

Stars having mass as big as 25 solar masses are prone to collapse to form black holes, during the process a part of the star spills out and most of the part collapse to form a black hole, after a period of time the collapsed core after emitting its all energy into space; obtain a certain finite density and hence size.