Thermal photon production in Gubser inviscid relativistic fluid dynamics

The Gubser solution to inviscid relativistic fluid dynamics is used to examine the role of transverse expansion on the energy spectrum of photons radiated by quark-gluon plasma. Transverse flow is shown to be a modest effect on the energy spectrum of photons as a whole, despite its large effect on rare high-energy photons produced at low temperatures. An exact expression is derived for the volume of the plasma as a function of its temperature. A simple formula is obtained for the energy spectrum of high-energy thermal photons, which is used to relate the inverse slope $T_{\text{eff}}$ of the photon spectrum at energy $E$ to the maximum temperature of the plasma $T_0$, finding $T_{\text{eff}}\approx T_0\mathrm{/}(1+\frac{5}{2}\frac{T_0}{E})$.