  Light emission by metals at room temperature is quenched by fast relaxation
processes. Nevertheless, Mooradian reported in 1969 the observation of
photoluminescence by metals pumped by a laser. Strikingly, while it is
currently at the heart of many promising applications, this phenomenon is still
poorly understood. In this work, we report a theory which reproduces
quantitatively previously published experimental data. We first provide a
general formula that relates the emitted power for a frequency, direction and
polarization state to a sum over all transitions involving matrix elements,
electronic distribution of all bands and the Green tensor. We then consider the
case of intraband recombination and derive a closed-form expression of the
emitted power depending only on macroscopic quantities. This formula, which is
a generalization of Kirchhoff's law, answers many of the open questions related
to intraband photoluminescence.
