One way to describe the entropy of black holes comes from partitioning momentum charge across fractionated intersecting brane systems. Here we construct \( \frac{1}{8} \) -BPS solutions by adding momentum to a maze of M2-brane strips stretched between M5 branes. Before the addition of momentum, the \( \frac{1}{4} \) -BPS supergravity solution describing the maze is governed by a master function obeying a complicated Monge-Ampère equation. Given such a solution, we show that one can add momentum waves without modifying the \( \frac{1}{4} \) -BPS M2-M5 background. Remarkably, these excitations are fully determined by a layered set of linear equations. The fields responsible for carrying the momentum are parameterized by arbitrary functions of a null direction, and have exactly the same structure as in brane world-volume constructions. The fact that the momentum and flux excitations of the M2-M5-P system are governed by a linear structure brings us one step closer to using supergravity solutions to capture the entropy of supersymmetric black-holes.
