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Register a new userViscosity to entropy ratio at extremality
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Assuming gauge theory realization at the boundary, we show that the viscosity to entropy ratio is 1/(4 pi) where the bulk is represented by a large class of extremal black holes in anti-de Sitter space. In particular, this class includes multiple R-charged black holes in various dimensions.
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The fireball concept of Rolf Hagedorn, developed in the 1960s, is an alternative description of hadronic matter. Using a recently derived mass spectrum, we use the transport model GiBUU to calculate the shear viscosity of a gas of such Hagedorn states, applying the Green-Kubo method to Monte-Carlo calculations. Since the entropy density is rising ad infinitum near $T_H$, this leads to a very low shear viscosity to entropy density ratio near $T_H$. Further, by comparing our results with analytic expressions, we find a nice extrapolation behavior, indicating that a gas of Hagedorn states comes close or even below the boundary $1/4pi$ from AdS-CFT.
The ratio of the shear viscosity to the entropy density is calculated for non-extremal Gauss-Bonnet (GB) black holes coupled to Born-Infeld (BI) electrodynamics in $5$ dimensions. The result is found to get corrections from the BI parameter and is analytically exact upto all orders in this parameter. The computations are then extended to $D$ dimensions.
The ratio of shear viscosity ($eta$) to entropy density ($s$) for an equilibrated system is investigated in intermediate energy heavy ion collisions below 100$A$ MeV within the framework of the Boltzmann-Uehling-Uhlenbeck (BUU) model . After the collision system almost reaches a local equilibration, the temperature, pressure and energy density are obtained from the phase space information and {$eta/s$} is calculated using the Green-Kubo formulas. The results show that {$eta$}/$s$ decreases with incident energy and tend towards a smaller value around 0.5, which is not so drastically different from the BNL Relativistic Heavy Ion Collider results in the present model.
The ratio of the shear viscosity ($eta$) to entropy density ($s$) for the intermediate energy heavy-ion collisions has been calculated by using the Green-Kubo method in the framework of the quantum molecular dynamics model. The theoretical curve of $eta/s$ as a function of the incident energy for the head-on Au+Au collisions displays that a minimum region of $eta/s$ has been approached at higher incident energies, where the minimum $eta/s$ value is about 7 times Kovtun-Son- Starinets (KSS) bound (1/4$pi$). We argue that the onset of minimum $eta/s$ region at higher incident energies corresponds to the nuclear liquid gas phase transition in nuclear multifragmentation.
Equilibration of highly excited baryon-rich matter is studied within the microscopic model calculations in A+A collisions at energies of BES, FAIR and NICA. It is shown that the system evolution from the very beginning of the collision can be approximated by relativistic hydrodynamics, although the hot and dense nuclear matter is not in local equilibrium yet. During the evolution of the fireball the extracted values of energy density, net baryon and net strangeness densities are used as an input to Statistical Model (SM) in order to calculate temperature $T$, chemical potentials $mu_B$ and $mu_S$, and entropy density $s$ of the system. Also, they are used as an input for the box with periodic boundary conditions to investigate the momentum correlators in the infinite nuclear matter. Shear viscosity $eta$ is calculated according to the Green-Kubo formalism. At all energies, shear viscosity to entropy density ratio shows minimum at time corresponding to maximum baryon density. The ratio dependence on $T, mu_B, mu_S$ is investigated for both in- and out of equilibrium cases.
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