Gravitational waves from a neutron star merging with a black hole carry the imprint of the intricate dynamics of spacetime. To decode that imprint, physicists compute scattering amplitudes, the quantum probabilities that two bodies fly apart at a given angle. But when the black hole spins and the neutron star deforms under tidal forces, the calculation turns into a maze of thousands of integrals. Each extra loop in a Feynman diagram adds another layer of complexity, and the infinite number of spin orders seemed to make the problem hopeless.

Now a key generator has appeared in this maze. John Smith and his colleagues noticed that all multiloop integrals describing scattering on a Kerr background can be generated from a single mathematical construction: the Kerr generating function. It depends on the black hole spin vector, and differentiating with respect to that vector yields the required tensor integrals. Instead of writing down bulky identities for each integral, you just differentiate one function. It is as if the maze had a thousand different doors, but they all shared a single master key.

The method turned out to be surprisingly powerful. The authors pushed the calculations to four loops (order $G^5$) for the leading nonlinear tidal operators and summed the spin dependence to all orders. The results are expressed in terms of hyperbolic cosine and generalized hypergeometric functions, compact formulas that hide all the complexity of rotation. The amplitudes split by the helicities of the exchanged gravitons (MHV, NMHV, $N^{2MHV}$), and in each sector the same structure emerges, generated by the same functions. This hidden simplicity means the maze has a regular layout: different paths are described by the same blueprint.

Previously, such calculations were limited to one or two loops or to spinless backgrounds. Now it is possible to obtain compact expressions for tidal scattering of a neutron star on a Kerr background up to four loops, with the black hole spin treated exactly to all orders. The key generator also opens doors to neighboring mazes: scattering of two spinning black holes, gravitational wave emission, and self-force corrections. If the method can be extended to these processes, the accuracy of gravitational wave models will improve, and with it our ability to hear the stories that neutron stars and black holes tell.