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holes - with masses several times that of the Sun - are possible, as they are
the only ones able to form in the final stages of stellar evolution. Although
they have many fascinating properties, these large black holes are not as
rich as their smaller cousins could be. The lighter the black hole the
greater its surface gravity - and the more interesting the associated
physical effects. This is simply due to the fact that Newton's gravitational
force is linearly dependent on mass but quadratically dependent on the
inverse distance (which is itself proportional to the Schwarzschild radius of
the black hole). In particular, the phenomenon of Hawking evaporation is
significant only in the case of small black holes: the tidal effect becomes
so great near the surface that the particle pairs produced by quantum vacuum
fluctuations may be broken, one particle falling into the black hole and the
other being projected outwards. This process has yet to be observed,
precisely because astrophysical black holes are too massive and therefore too
cold, but it is certainly one of the most important predictions of quantum
field theory in curved space-time. Contrary to the usual ideas of general
relativity, black holes are capable of emitting particles. They can even be
very hot and very bright if their mass is sufficiently small. Indeed, the
principles of thermodynamics apply to black holes, the essential variables
being temperature, entropy and internal energy, as opposed to surface
gravity, area and mass in the case of general relativity.

Where can we find mini black holes?

The absence of notable excesses of particles in cosmic radiation - especially
in the form of antiprotons or gamma rays - compared with the fluxes expected
in a "standard" astrophysics context allows strict constraints to be placed
on the density of black holes evaporating in today's universe. In particular,
it can be deduced that their contribution to the total mass of the universe
is today no higher than one ten millionth. As these small black holes are
likely to have been produced in the early cosmos thanks to the fluctuations
in density present at that time - and with masses that were arbitrarily low -
it is possible to obtain vital information about the universe's degree of
inhomogeneity shortly after the period of inflation. This route of
investigation is all the more remarkable in that the relevant scales for the
black holes of the early universe are completely beyond the usual observables
of cosmology, namely the 3K background radiation and large-scale structure.
There is therefore a genuine complementarity between these approaches. Many
cosmological scenarios - involving phase transitions, the breaking of scale
invariance, blue power spectra, positive running of the spectral index of
scale fluctuations, phases of double inflation, topological defects,
collisions of bubbles of "real" vacuum in a background of "false" vacuum and
softening of the equation of state - may be excluded or severely constrained
by the study of small black holes.

Evaporation of a black hole

In addition to these astrophysical and cosmological aspects, there is another
route of investigation that is particularly promising for microscopic black
holes, namely at particle accelerators. In response to the persistent problem
of hierarchy - why is the Planck scale 16 orders of magnitude higher than the
electroweak scale? - a hypothesis put forward a few years ago offers a neat
and efficient lead: the existence of large extra dimensions. The novelty of
this idea lies in the fact that it is no longer necessary to assume that
these dimensions are of sizes close to the Planck length (~10-33cm). Rather,
they can be as large as around a millimetre if we suppose that the fields of
matter live in the 3+1 dimensional hypersurface of our 3-brane and that only
gravity can benefit from new dimensions. The constraints (~10-16cm ) usually
derived via the interactions of gauge bosons in extra dimensions can
therefore be ignored and only experiments involving the direct measurement of
Newtonian gravity put limits on the size of extra dimensions to a value of
less than a few tenths of a millimetre. Using such an approach, the
traditional Planck energy, EPI~1019GeV, is no more than an effective scale
and the real D-dimensional fundamental Planck scale is given by ED =
(EPI2/VD-4)1/(D-2), where VD-4 is the volume associated with the D-4 extra
dimensions. For D=10 and radii associated with the extra dimensions of the
Fermi scale, we obtain ED~TeV. If this model has any meaning, it is
effectively a natural choice (and not an arbitrary one based on
phenomenological motivations) because it essentially resolves the problem of
hierarchy. This approach uses the geometrical properties of space to link
completely different energy scales.

A spectacular consequence of such a model is the possibility of being able to
produce black holes with the next generation of particle colliders. If the
centre-of-mass energy of two elementary particles is indeed higher than the
Planck scale ED, and their impact parameter b is lower than the Schwarzschild
radius RH, a black hole must be produced. If the Planck scale is thus in the
TeV range, the 14 TeV centre-of-mass energy of the Large Hadron Collider
(LHC) could allow it to become a black-hole factory with a production rate as
high as about one per second. Many studies are underway to make a precise
evaluation of the cross-section for the creation of black holes via parton
collisions, but it appears that the naive geometric approximation σ~πR2H is
quite reasonable for setting the orders of magnitude.

Black hole temperature graph

The possible presence of extra dimensions would be doubly beneficial for the
production of black holes. The key point is that it allows the Planck scale
to be reduced to accessible values, but it also allows the Schwarzschild
radius to be significantly increased, thus making the condition b<RH
distinctly easier to satisfy. It is important to note that the resulting mini
black holes have radii that are much smaller (of the order of 10-4fm in the
case of those that can be expected from the LHC) than the size of extra
dimensions, and that they can therefore be considered as totally immersed in
a D-dimensional space, which has, to a good approximation, a time dimension
and D-1 non-compact space dimensions. The black hole thus acts like a
quasi-selective source of S waves and sees our brane in the same way as the
"bulk" associated with the extra dimensions. As the particles residing in the
brane greatly outnumber those living in the bulk (essentially gravitons), the
black hole evaporates into particles of the Standard Model. Its lifetime is
very short (of the order of 10-26s) and its temperature (typically about 100
GeV here) is much lower than it would be with the same mass in a
four-dimensional space. The black hole nevertheless retains its
characteristic spectrum in the form of a quasi-thermal law peaked around its
temperature. From the point of view of detection, it is not too difficult to
find a signature for such events: they have a high multiplicity, a large
transverse energy, a "democratic" coupling to all particles and a rapid
increase in the production cross-section with energy.

ATLAS detector simulation

Particle physics and mini black holes

At first glance the production of black holes in colliders could be bad news.
It could mean the end of particle physics since the presence of a horizon
would obscure all the microphysics processes that could occur behind it.
However, it would in fact open up very good opportunities.

First of all the reconstruction of temperature (determined by the energy
spectrum of the particles emitted when the black hole evaporates) as a
function of mass (determined by the total energy deposited) allows
information to be gained about the dimensionality of space- time. In the case
of Planck scales close to the TeV mark, the number of extra dimensions could
thus be revealed quite easily by the characteristics of the emitted
particles. However, one can go further. In particular, quantum gravity
effects could be revealed, as behaviour during evaporation in the Planck
region is sensitive to the details of the gravitational theory used.

Approaches of the Gauss-Bonnet type, which include quadratic terms in scalar
curvature in the Lagrangian, are good candidates for a description beyond
general relativity as they can be supported both by theoretical arguments
(heterotic strings in particular) and by phenomenological arguments (Taylor
expansion in curvature). In such a case, the coupling constant of the
Gauss-Bonnet term, namely the quantum character of the gravitational theory
used (and the link with the underlying string theory) can also be
reconstructed and the LHC would become a very valuable tool for studying
speculative gravitation models.

Other promising avenues are also being investigated for new physics. Firstly,
the black holes formed may be excellent intermediate states for highlighting
new particles. When the collision energy is higher than the Planck scale ED,
the cross-section for the creation of black holes is quite large (~500 pbarn)
and has no suppression factor. Moreover, when the temperature of the black
hole is higher than the mass of a particle, the particle must be emitted
during evaporation in proportion to its number of internal degrees of
freedom. There is thus a definite potential for the search for the Higgs or
for supersymmetric particles in the evaporation products of black holes,
possibly with cross-sections much greater than for the direct processes.
Finally, taking account of a D-dimensional cosmological constant also
modifies the evaporation law. If the constant is sufficiently high - which is
possible without contradicting the low value measured in our brane - the
temperature and the coupling coefficients with the entities emitted could be
the signature of this particular structure of space-time. It would be quite
neat and certainly surprising that a measurement of the cosmological constant
in the bulk should come from the LHC!

Microscopic black holes are thus a paradigm for convergence. At the
intersection of astrophysics and particle physics, cosmology and field
theory, quantum mechanics and general relativity, they open up new fields of
investigation and could constitute an invaluable pathway towards the joint
study of gravitation and high-energy physics. Their possible absence already
provides much information about the early universe; their detection would
constitute a major advance. The potential existence of extra dimensions opens
up new avenues for the production of black holes in colliders, which would
become, de facto, even more fascinating tools for penetrating the mysteries
of the fundamental structure of nature.

Postscript

It should be stated, in conclusion, that these black holes are not dangerous
and do not threaten to swallow up our already much-abused planet. The
theoretical arguments and the obvious harmlessness of any black holes that,
according to these models, would have to be formed from the interaction of
cosmic rays with celestial bodies, mean that we can regard them with perfect
equanimity.

Further reading

N Arkani-Hamed, S Dimopoulos and G R Dvali 1998 Phys. Lett. B429 257.

A Barrau et al. 2002 Astronom. Astrophys.388 676.

A Barrau et al. 2004 Phys. Lett. B584 114.

S Dimopoulos and G Landsberg 2001 Phys. Rev. Lett.87 161602.

J L Feng and A D Shapere 2002 Phys. Rev. Lett.88 021303.

S B Giddings and S Thomas 2002 Phys. Rev. D65 056010.

P Kanti 2004 Int. J. Mod. Phys. (in press) www.arxiv.org/hep-ph/0402168. G
Landsberg 2002 Phys. Rev. Lett. 88 181801.

Author: Aurélien Barrau and Julien Grain, Grenoble Laboratory of Subatomic
Physics and Cosmology (CNRS/Joseph Fourier University).