Interaction of a TeV scale black hole with the quark-gluon plasma at CERN LHC

If the fundamental Planck scale is near 1 TeV, then parton collisions with a 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 $\sqrt{s}=14\mathrm{}\mathrm{TeV}$ and for a lead-lead collision at $\sqrt{s}=5.5\mathrm{}\mathrm{TeV}$ at CERN LHC. As the parton energy density is much higher in 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 absorb the quark-gluon plasma formed at LHC. The accretion rate of the black hole is proportional to the energy density of the plasma and the evaporation rate is proportional to $T^{4+d},$ where d is the number of extra dimensions, so it is easy to determine what energy density is necessary to stabilize the black hole. The question we address here is how to make a reasonable estimate of the energy density of the plasma in the expected out of equilibrium initial conditions at LHC. For this purpose we use a combination of PQCD and a reasonable ansatz for the single-particle distribution functions of partons. Using this approach, we find that the energy density of partons formed in lead-lead collisions at LHC is about 500 ${\mathrm{G}\mathrm{e}\mathrm{V}/\mathrm{f}\mathrm{m}}^3$, leading to the rate of absorption for one of these black holes being much smaller than the rate of evaporation. More precisely, we show that for the black hole mass to increase via parton absorption the typical energy density of quarks and gluons should be of the order of ${10}^{10}{\mathrm{G}\mathrm{e}\mathrm{V}/\mathrm{f}\mathrm{m}}^3.$ We also find that the typical lifetime of the black hole formed at LHC is found to be a small fraction of a $\mathrm{fm}/c.\mathrm{}$