Micro Black Hole - Minimum Mass of A Black Hole

Minimum Mass of A Black Hole

In principle, a black hole can have any mass equal to or above the Planck mass (about 22 micrograms). To make a black hole, one must concentrate mass or energy sufficiently that the escape velocity from the region in which it is concentrated exceeds the speed of light. This condition gives the Schwarzschild radius, where G is Gravitational constant and c is the speed of light, of a black hole of mass M. On the other hand, the Compton wavelength, where h is Planck's constant, represents a limit on the minimum size of the region in which a mass M at rest can be localized. For sufficiently small M, the reduced Compton wavelength (, where ħ is Dirac's constant) exceeds half the Schwarzschild radius, and no black hole description exists. This smallest mass for a black hole is thus approximately the Planck mass.

Some extensions of present physics posit the existence of extra dimensions of space. In higher-dimensional spacetime, the strength of gravity increases more rapidly with decreasing distance than in three dimensions. With certain special configurations of the extra dimensions, this effect can lower the Planck scale to the TeV range. Examples of such extensions include large extra dimensions, special cases of the Randall-Sundrum model, and string theory configurations like the GKP solutions. In such scenarios, black hole production could possibly be an important and observable effect at the LHC. It would also be a common natural phenomenon induced by the cosmic rays.

All this asumes that the theory of general relativity remains valid at these small distances. If it does not, then other, presently unknown effects, will limit the minimum size of a black hole.