Analogue surface gravity near the QCD chiral phase transition

Using the formalism of relativistic acoustic geometry we study the expanding chiral fluid in the regime of broken chiral symmetry near the QCD chiral phase transition temperature _Tc$T_{\mathrm{c}}$. The dynamics of pions below _Tc$T_{\mathrm{c}}$ is described by the equation of motion for a massless scalar field propagating in curved spacetime similar to an open FRW universe. The metric tensor depends locally on the soft pion dispersion relation and the four-velocity of the fluid. In the neighbourhood of the critical point an analogue trapped region forms with the analogue trapped horizon as its boundary. We show that the associated surface gravity diverges near the critical point as κ∼(_Tc−T)⁻¹$\kappa \sim {(T_{\mathrm{c}}-T)}^{-1}$. Hence, if the horizon forms close to the critical temperature the analogue Hawking temperature may be comparable with or even larger than the background fluid temperature.