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:
“After decades of unappreciated drudgery, American women just don’t do housework any more—that is, beyond the minimum that is required in order to clear a path from the bedroom to the front door so they can get off to work in the mourning.”
—Barbara Ehrenreich (20th century)
“Masterpieces are not single and solitary births; they are the outcome of many years of thinking in common, of thinking by the body of the people, so that the experience of the mass is behind the single voice.”
—Virginia Woolf (1882–1941)
“Don’t look now, God, we’re all right.
All the suicides are eating Black Bean Soup;
the Dalmatians, our turnip, our spotted parasite
snoozles in her chair.”
—Anne Sexton (1928–1974)
“Wondrous hole! Magical hole! Dazzlingly influential hole! Noble and effulgent hole! From this hole everything follows logically: first the baby, then the placenta, then, for years and years and years until death, a way of life. It is all logic, and she who lives by the hole will live also by its logic. It is, appropriately, logic with a hole in it.”
—Cynthia Ozick (b. 1928)