The possibility of producing microscopic black holes at the Large Hadron
Collider (LHC) is one of the most exciting consequences of “brane world”
models developed over the past 15 years or so. The purpose of this presentation
is to outline the theories behind this intriguing possibility: gravitational
theories in which the energy scale of quantum gravity is much lower
than the conventional value of 1019 GeV, and may possibly be as low as a
few TeV. I will also describe some of the features of black hole creation
and evolution in these low-scale quantum gravity theories. Finally we link
the theoretical modelling to experimental searches for black holes at the
LHC.
Microscopic black hole decay
We now consider what happens to a microscopic black hole formed by
particle collisions at the LHC. When initially created, the black hole will
be highly asymmetric and will have attached gauge field hair arising from
the gauge field quantum numbers of the colliding partons. The black hole
will also be rapidly rotating, due to the initial angular momentum. Let's assume that the initial energy of the
black hole is at least a few times greater than the quantum gravity scale
E∗, so that its geometry can be described in terms of general relativity. This is the semi-classical approximation
- we consider quantum processes on the classical black hole background.
The subsequent evolution of the black hole can be described in terms of
four stages.
Balding phase
The black hole sheds its asymmetries and attached gauge
field hair. This phase is often modelled as part of the black hole production
process. At the end of this phase the black hole is still rapidly
rotating.
Spin-down phase
The black hole emits Hawking radiation, losing mass
and angular momentum. At the end of this phase the black hole is
not rotating.
Schwarzschild phase
The black hole is now spherically symmetric and
continues to emit Hawking radiation.
Planck phase When the energy of the black hole is of the same order as the
quantum gravity scale E∗, its geometry can no longer be described
by general relativity and the full details of quantum gravity effects
(which are ignored in the semi-classical approximation) become important.
We now briefly discuss each of these phases.
Balding phase
One of the key questions concerning the balding phase is how much of
the initial energy of the colliding particles is shed in gravitational radiation
as the black hole forms. Both the colliding shock wave model and
full numerical relativity calculations outlined above give upper bounds on
this and therefore lower bounds on the mass of the black hole. For example,
for head-on colliding shock waves, the energy of the black hole is at
least 70% of the initial energy for collisions in four space-time dimensions,
and at least 58% of the initial energy for collisions in eleven space-time
dimensions. As an example of the results from numerical relativity,
four-dimensional calculations indicate that about 50% of the initial energy
of the colliding particles is radiated away in the ultra-relativistic limit.
The emitted gravitational radiation has also been studied by a number of
other approaches.
The second aspect of the balding phase is the shedding of charges and
gauge field hair. This has not received much attention in the literature.
In particular, QCD effects are likely to be very important at the LHC, but
there is little work on this. The effect of electric charge on the formation
process has been studied in numerical relativity, and upper bounds on
the amount of electromagnetic as well as gravitational radiation have been
computed.
Naively one would expect that any electric charge left on the black hole
would rapidly discharge due to Schwinger pair production. However,
this assumption is based on conventional four-dimensional gravity models
where electromagnetic interactions are many orders of magnitude stronger
than gravitational interactions. In higher-dimensional gravity models with
strong gravity, the loss of electric charge is not so rapid.
Quantum black holes
Our focus in this brief note has been the “standard” model of microscopic
black hole production and decay at the LHC, in the context of the ADD
brane-world scenario. In this model, the black hole is semi-classical: the
metric is classical and described by general relativity, and the black hole
emits quantum Hawking radiation. This semi-classical approximation
breaks down when the black hole energy is roughly E∗, the energy scale at
which the details of the unknown theory of quantum gravity become important.
Meade and Randall have argued that, in order for the black
hole to be described by a classical metric, it must be the case that the Compton
wavelengths of the colliding particles lie within the event horizon of
the formed black hole. This implies that the black hole energy should be at
least an order of magnitude larger than E∗ for the semi-classical approximation
to be valid.
In the absence of a full theory of quantum gravity, there have been attempts
in the literature to study fully quantum black holes with energies
close to E∗, as well to refine the semi-classical picture to incorporate
quantum gravity effects [36]. Fully quantum black holes do not decay thermally,
but instead emit just a few particles. Particle physics symmetries are
used to constrain the decay processes.
Experimental searches
There are a number of event generators simulating black hole processes at
the LHC. The LHC experimental groups use CHARYBDIS2 and BlackMax for simulating semi-classical black holes and QBHfor the simulation of quantum black holes. Black hole events typically
have high primary particle multiplicity with large missing transverse momentum.
At the time of writing no evidence for either semi-classical or quantum
black holes has been observed at the LHC. These null results
have enabled the LHC experimental groups to set lower bounds on
the higher-dimensional quantum gravity scale E∗. ATLAS rule out semiclassical
black holes having masses lower than about 4 TeV/c2
for six extra
dimensions and E∗ about 2 TeV, while CMS have slightly higher lower
bounds on the semi-classical black hole mass for the same values of E∗.
CMS also rule out quantum black holes with masses lower than about 5 − 6
TeV/c2
for E∗ = 2 − 5 TeV.
Conclusions
We have briefly reviewed the ADD large extra dimensions scenario, in
which the energy scale of quantum gravity, E∗, may be as low as a few
TeV. This raises the exciting possibility of probing quantum gravity effects
at the LHC. Of the many possible strong gravity processes, those involving
microscopic black holes will be some of the most spectacular. Our focus in
this note has been a semi-classical model of microscopic black hole production
and decay, with the geometry described by general relativity and
quantum Hawking radiation being emitted from the black hole. We have
also discussed the validity of this model and recent work on describing
fully quantum black holes. To date, there has been no experimental evidence
for black holes at the LHC. However, this does not diminish the importance
of searching for them: the non-observation results have set lower
bounds on the energy scale E∗, constraining the elusive theory of quantum gravity.
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