Hawking radiation of relativistic particles from black strings

We study Hawking radiation of relativistic particles from uncharged and charged black strings in $3+1$ dimensions in detail. We use the method of quantum tunneling in the framework of the Hamilton–Jacobi approach. We show that the radial function of the action allows calculating the tunneling rate of the emitted relativistic particles. Using the Boltzmann formula, we derive the Hawking temperatures of uncharged and charged black strings. We discuss the influence of the temporal contribution to the tunneling rate.