We investigate the temporal evolution of electronic states in strontium iridate Sr$_2$IrO$_4$. The time resolved photoemission spectra of intrinsic, electron doped and the hole doped samples are monitored in identical experimental conditions. Our data on intrinsic and electron doped samples, show that primary doublon-holon pairs relax near to the chemical potential on a timescale shorter than $70$ fs. The subsequent cooling of low energy excitations takes place in two step: a rapid dynamics of $cong120$ fs is followed by a slower decay of $cong 1$ ps. The reported timescales endorse the analogies between Sr$_2$IrO$_4$ and copper oxides.
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