If the fundamental Planck scale is near a TeV, then parton collisions with
high enough center-of-mass energy should produce black holes. The production
rate for such black holes has been extensively studied for the case of a
proton-proton collision at \sqrt s = 14 TeV and for a lead-lead collision at
\sqrt s = 5.5 TeV at LHC. As the parton energy density is much higher at
lead-lead collisions than in pp collisions at LHC, one natural question is
whether the produced black holes will be able to absorb the partons formed in
the lead-lead collisions and eventually `eat' the quark-gluon plasma formed at
LHC. In this paper, we make a quantitative analysis of this possibility and
find that since the energy density of partons formed in lead-lead collisions at
LHC is about 500 GeV/fm^3, the rate of absorption for one of these black holes
is much smaller than the rate of evaporation. Hence, we argue that black holes
formed in such collisions will decay very quickly, and will not absorb very
many nearby partons. More precisely, we show that for the black hole mass to
increase via parton absorption at the LHC the typical energy density of quarks
and gluons should be of the order of 10^{10} GeV/fm^3. As LHC will not be able
to produce such a high energy density partonic system, the black hole will not
be able to absorb a sufficient number of nearby partons before it decays. The
typical life time of the black hole formed at LHC is found to be a small
fraction of a fm/c.Comment: 7 pages latex (double column), 3 eps figure