Theoretical study of the black hole production, in high-energy collisions,
goes back to the study of Penrose (1974) the mechanism
of black hole production by LHC introduced by Giddings and
Thomas (2002) and Dimopoulos and Landsberg (2001).
Production of black holes by particle accelerators is an even more exciting
possibility, when it comes to producing high-energies, no device out does accelerators
such as LHC and Tevatron. These machines accelerate subatomic particles to velocities
exceedingly close to the speed of light. These particles then have enormous
kinetic energies. At the LHC, a proton will reach energy of roughly TeV (Giddings
and Thomas, 2002; Dimopoulos and Landsberg, 2001;
Anchordoqui et al., 2003). According to Einstein
special relativity this energies are equivalent to a mass of 10-23
k.g. when two particles collide at close range, their energy in concentrated
into a tiny region of space. Black hole factories are microscopic, comparison
in size to elementary particles, they could evaporate shortly after they formed,
because the emission carries off energy, the mass of black hole tend to decrease.
Therefore a black hole factory is highly unstable. The evaporation of these
holes would leave very distinctive imprints on the detectors. Typical collisions
produce moderate numbers of high-energy particles, but decaying black hole is
different. According to Hawking (1975), the black hole
radiates a large number of particles and the prospect of producing black holes
on Earth may strike. How do we know that would safely decay, as hawking predicted,
instead of continuing to grow, eventually consuming the entire planet? Recently
we have calculated the hawking radiation of the black hole at a higher dimensional
space-time (Dehghani and Farmany, 2009a, b;
Farmany et al., 2008). Here, we review the new
approaches to calculating the black hole entropy and we suggest a new method
for calculation of the lifetime of the LHC-black hole.
Let, we begin with a black hole that live on d-dimensional space time. A d-dimensional (Schwarzschild) black hole as LHC-black hole is defined by:
and Gd is the d-dimensional Newton constant. Consider a black hole factory as a d-dimensional cube of size equal to twice its radius (Schwarzschild radius) rs the uncertainty in the position of a hawking particle, during the emission, is:
Using the usual uncertainty principle the uncertainty in the energy of hawking particle is:
is the mass in the Planck unit, Mp is the d-dimensional Planck mass.
ΔE is identified with the temperature of black hole radiation. Setting
the black hole radiation mass m to d-3/4π it is easy to obtain the temperature
of the black hole in d-dimensional space-time:
The evaporation of black hole would leave very distinctive imprints on the
detectors and temperature of such black hole could be calculated. To study the
quantum gravity effects in the hawking temperature, one can take into account
the generalized uncertainty principle. Generalized uncertainty principle have
been the subject of much interesting works over the years and a lot of papers
have been appeared in which that the usual uncertainty is modified at the framework
of microphysics as (Farmany et al., 2007; Farmany,
where, lpl is the Planck length. The term:
in Eq. 5 show the gravitational effects to usual uncertainty
principle. In the canonical quantum gravity the area of black hole factory is
quantized as .
For this reason we must obtain the lower bound on the black hole factory radius.
Consider a quantum black hole factory, an attempt to measure the radius of the
black hole, more precisely that is, to make R small-thus resulting in an increase
of Δp, but according to Eq. 5 for detection of small
distances by going to very high momenta, the behavior of Heisenberg microscope
changes and a lower bound on the (Schwarzschild) radius rs could
be obtained. Setting rs as Δxi and inverting Eq.
5 we obtain:
Comparing Eq. 2, 4 with 6
we obtains the Hawking radiation of black hole factory:
Comparing Eq. 4 with Eq. 7 we find that the temperature of hawking radiation of black hole factory is hotter than the hawking calculations:
Equation 8 shows that hawking temperature of LHC-black hole is hotter than the hawking temperature.
Let, we focus on the lifetime of the LHC-black hole. The black hole radiation losses the mass of black hole as:
The LHC-black hole will evaporates to receives the Planck mass. In this step, the LHC-black hole changes to a Higgs particle that have a Planck mass, so the lifetime of the black hole is:
where, g is the number of particles that are emitted by LHC-black hole 3<g<100.