Thermal Emission of Gravitational Waves from Weak to Strong Coupling

We study the production of gravitational waves by a thermalized plasma of $\mathcal N$=4 Supersymmetric Yang Mills matter. We focus on the large number of colors limit, $N_c\rightarrow \infty$, and compute the spectrum of gravitational waves both for infinitely large and infinitesimally small values of the 't Hooft coupling constant $\lambda$. In the $\lambda\rightarrow \infty$ limit we employ the gauge/gravity duality to compute the emission rate via the analysis of Energy-Momentum tensor thermal correlators. In the $\lambda \rightarrow 0$ limit we employ state-of-the-art perturbative analyses to calculate the complete leading order emission rate. By comparing these extreme limits, we bracket the magnitude of the spectrum induced by this source of gravitational waves. Embedding our results in a cosmological evolution model, we find qualitative and quantitative similarities between the strong coupling spectrum and the extrapolation of the perturbative results up to an intermediate value of the coupling, after an appropriate re-scaling of the effective number of degrees of freedom. We comment on how our results can help better understand the contribution of thermalized matter to the stochastic spectrum of gravitational waves.