Editing Micro black hole (section)

== Minimum mass of a black hole ==
In an early speculation, [[Stephen Hawking]] conjectured that a [[black hole]] would not form with a mass below about {{val|e=-8|u=kg}} (roughly the [[Planck mass]]).<ref name="verylowmass" /> 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]].

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 dimension]]s, 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 [[Large Hadron Collider]] (LHC).<ref name="carr"/><ref name="giddings"/><ref name="dimopoulos"/><ref name="NYT"/><ref name="courier"/>
It would also be a common natural phenomenon induced by [[cosmic rays]].

All this assumes that the theory of [[general relativity]] remains valid at these small distances. If it does not, then other, currently unknown, effects might limit the minimum size of a black hole. Elementary particles are equipped with a quantum-mechanical, intrinsic [[angular momentum]] ([[Particle spin|spin]]). The correct conservation law for the total (orbital plus spin) angular momentum of matter in curved spacetime requires that spacetime is equipped with [[Torsion tensor|torsion]]. The simplest and most natural theory of gravity with torsion is the [[Einstein–Cartan theory]].<ref>{{cite journal |last1=Sciama |first1=Dennis W. |author-link=Dennis Sciama |year=1964 |title=The physical structure of general relativity |journal=Reviews of Modern Physics |volume=36 |issue=1 |pages=463–469 |doi=10.1103/revmodphys.36.463 |bibcode=1964RvMP...36..463S}}</ref><ref>{{cite journal |last1=Kibble |first1=Tom W.B. |author-link=Tom Kibble |year=1961 |title=Lorentz invariance and the gravitational field |doi=10.1063/1.1703702 |journal=Journal of Mathematical Physics |volume=2 |issue=2 |pages=212–221 |bibcode = 1961JMP.....2..212K}}</ref> Torsion modifies the [[Nonlinear Dirac equation|Dirac equation]] in the presence of the gravitational field and causes [[fermion]] particles to be spatially extended. In this case the spatial extension of fermions limits the minimum mass of a black hole to be on the order of {{val|e=16|u=kg}}, showing that micro black holes may not exist. The energy necessary to produce such a black hole is 39&nbsp;orders of magnitude greater than the energies available at the Large Hadron Collider, indicating that the LHC cannot produce mini black holes. But if black holes are produced, then the theory of general relativity is proven wrong and does not exist at these small distances. The rules of general relativity would be broken, as is consistent with theories of how matter, space, and time break down around the [[event horizon]] of a black hole. This would prove the spatial extensions of the fermion limits to be incorrect as well. The fermion limits assume a minimum mass needed to sustain a black hole, as opposed to the opposite, the minimum mass needed to start a black hole, which in theory is achievable in the LHC under some conditions.<ref>{{cite news |first=Stephen |last=Hawking |author-link=Stephen Hawking |url=http://www.msnbc.com/morning-joe/steven-hawking-warns-doomsday |title=New doomsday warning |publisher=MSNBC}}</ref><ref>{{cite journal |author-link=Nikodem Popławski |first=Nikodem J. |last=Popławski |year=2010 |title=Nonsingular Dirac particles in spacetime with torsion |journal=Physics Letters B |volume=690 |issue=1 |pages=73–77 |doi=10.1016/j.physletb.2010.04.073 |arxiv=0910.1181 |bibcode=2010PhLB..690...73P}}</ref>