Net-charge fluctuation in Au+Au collisions at energies available at the Facility for Antiproton and Ion Research using the UrQMD model

We have studied the dynamical fluctuation of net-charge of hadrons produced in Au+Au collisions at energies that in near future will be available at the Facility for Antiproton and Ion Research (FAIR). Data simulated by a microscopic transport model based on ultra-relativistic quantum molecular dynamics are analyzed for the purpose. The centrality and pseudorapidity dependence of the net-charge fluctuation of hadrons are examined. Our simulated results are compared with the results available for nucleus-nucleus collision experiments held at similar energies. The gross features of our simulated results on net-charge fluctuations are found to be consistent with the experiment. At incident beam energy $E_{\rm lab}=10A$ GeV the magnitude of net-charge fluctuation is very large, and in comparison with the rest its centrality dependence appears to be a little unusual. The effect of global charge conservation is expected to be very crucial at FAIR energies. The charge fluctuations measured with varying pesudorapidity window size depend on the collision centrality. The dependence is however exactly opposite in nature to that observed in the Pb+Pb collision at $\sqrt{s_{_{NN}}}=2.76$ TeV.