QNMs for Lifshitz black holes had only been studied for scalar field fluctuations. Here we computed them for gravitational fluctuations. These are more interesting than scalar ones because the corresponding fluctuations couple to conserved currents in the dual field theory. This is a computation that has been missing in the literature and connects work done in the past on Lifshitz black branes with the developments of Lifshitz hydrodynamics. It revealed big differences in terms of dissipation in the two models giving rise to Lifshitz black branes, which was not anticipated.
Being interested in the thermalisation of these systems and the radius of convergence of the associated Lifshitz hydrodynamics, we had to take a step back and first study the radius of convergence of charged relativistic systems. We found a strong dependence of the radius of convergence on the charge. In this work we also studied the phenomenon of pole-skipping, and showed that the value of the frequencies at which it occurs can be determined by analysing the behaviour of the fluctuations at the horizon. A similar behaviour is expected for Lifshitz systems given that both models carry charge. A preliminary study of pole-skipping supports this statement.
Many of the calculations involving QNMs within holography involved numerical calculation. In an attempt to understand better the behaviour of hydrodynamic modes in holography and in particular the origin of the differences in the two Lifshitz models, we developed a formalism that can extract the hydrodynamics modes analytically using properties of the horizon of the corresponding black hole. This has so far been done in the context of asymptotically Anti-de-Sitter spacetime where the duality is better understood and could now be extended to the Lifshitz case in order to understand where the difference in the 2 Lifshitz models is coming from.
In terms of further understanding the capabilities of the Large-D limit of general relativity and the connections between gravity and fluids, we have performed numerical simulations within this framework showing that gravitational theories can develop a (driven) turbulent regime, which in fact follows the celebrated Kolmogorov scaling for driven turbulence in fluids.
Last but not least, we have also studied holographic superfluids, where we have constructed Abrikosov vortical lattices. Repeating this for Lifshitz superconductor will be an interesting next step.
