The recently suggested interpretation P. Castorina, D. Kharzeev, and H. Satz, [Eur. Phys. J. C 52, 187 (2007).] of the universal hadronic freeze-out temperature $T_f$ ($\simeq 170\mathrm{MeV}$)—found for all high-energy scattering processes that produce hadrons $e^{+}{e}^{-}$, $pp$, $p\overline{p}$, $\pi p$, etc., and $N{N}^{\prime }$ (heavy-ion collisions)—as an Unruh temperature triggers here the search for the gravitational black hole (BH) that in its near-horizon approximation better simulates this hadronic phenomenon. To identify such a BH we begin our gravity-gauge theory phenomenologies matching by asking the question: which BH behind that Rindler horizon could reproduce the experimental behavior of $T_f(\sqrt{s})$ in $N{N}^{\prime }$, where $\sqrt{s}$ is the collision energy? Provided certain natural assumptions hold, we show that the exact string BH turns out to be the best candidate (as it fits the available data on $T_f(\sqrt{s})$) and that its limiting case, the Witten BH, is the unique candidate to explain the constant $T_f$ for all elementary scattering processes at large energy. We also are able to propose an effective description of the screening of the hadronic string tension $\sigma ({\mu }_b)$ due to the baryon density effects on $T_f$.

• Received 4 March 2008

DOI:https://doi.org/10.1103/PhysRevD.77.124034