Understanding the interaction of massive black hole binaries with their gaseous environment is crucial since at sub-parsec scales the binary is too wide for gravitational wave emission to take over and to drive the two black holes to merge.
The outcome of the binary-disc interaction in terms of binary semi-major axis evolution has been recently debated and is still unclear mainly due to numerical limitations, i.e. fixed orbit binaries or lack of resolution inside the cavity carved by the binary in its circumbinary disc.
In this talk I will present our results on the interaction between a massive black hole binary and a circumbinary disc using hyper-Lagrangian 3D hydrodynamics simulations.
These results are especially important for massive black hole binaries in the LISA and PTA band.