Black hole interactions at large $D$: brane blobology

In the large dimension ($D$) limit, Einstein's equation reduces to an effective theory on the horizon surface, drastically simplifying the black hole analysis. Especially, the effective theory on the black brane has been successful in describing the non-linear dynamics not only of black branes, but also of compact black objects which are encoded as solitary Gaussian-shaped lumps, {\it blobs}. For a rigidly rotating ansatz, in addition to axisymmetric deformed branches, various non-axisymmetric solutions have been found, such as black bars, which only stay stationary in the large $D$ limit. In this article, we demonstrate the blob approximation has a wider range of applicability by formulating the interaction between blobs and subsequent dynamics. We identify that this interaction occurs via thin necks connecting blobs. Especially, black strings are well captured in this approximation sufficiently away from the perturbative regime. Highly deformed black dumbbells and ripples are also found to be tractable in the approximation. By defining the local quantities, the effective force acting on distant blobs are evaluated as well. These results reveal that the large $D$ effective theory is capable of describing not only individual black holes but also the gravitational interactions between them, as a full dynamical theory of interactive blobs, which we call {\it brane blobology}.