# Waves on Mazes

Iosif Bena, Raphaël Dulac, Anthony Houppe, Dimitrios Toulikas, Nicholas P. Warner

Iosif Bena, Raphaël Dulac, Anthony Houppe, Dimitrios Toulikas, Nicholas P. Warner

**22/4/24**Published in : arXiv:2404.14477

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.