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.
Read more about this topic: Micro Black Hole
Famous quotes containing the words minimum, mass, black and/or hole:
“There are ... two minimum conditions necessary and sufficient for the existence of a legal system. On the one hand those rules of behavior which are valid according to the system’s ultimate criteria of validity must be generally obeyed, and on the other hand, its rules of recognition specifying the criteria of legal validity and its rules of change and adjudication must be effectively accepted as common public standards of official behavior by its officials.”
—H.L.A. (Herbert Lionel Adolphus)
“If all feeling for grace and beauty were not extinguished in the mass of mankind at the actual moment, such a method of locomotion as cycling could never have found acceptance; no man or woman with the slightest aesthetic sense could assume the ludicrous position necessary for it.”
—Ouida [Marie Louise De La Ramée] (1839–1908)
“This is the end, the redemption from Wilderness, way for the Wonderer, House sought for All, black handkerchief washed clean by weeping—page beyond Psalm—Last change of mine and Naomi—to God’s perfect Darkness— Death, stay thy phantoms!”
—Allen Ginsberg (b. 1926)
“During Prohibition days, when South Carolina was actively advertising the iodine content of its vegetables, the Hell Hole brand of ‘liquid corn’ was notorious with its waggish slogan: ‘Not a Goiter in a Gallon.’”
—Administration in the State of Sout, U.S. public relief program (1935-1943)