# Generalized Near Horizon Extreme Binary Black Hole Geometry

## TL;DR

This paper introduces a new exact vacuum solution describing the near horizon geometry of two co-rotating, extreme Kerr black holes, revealing a complex structure with a localized strut and two separate NHEK throats.

## Contribution

It provides the first explicit vacuum solution for the near horizon region of two non-identical, co-rotating extreme Kerr black holes with detailed geometric and physical analysis.

## Key findings

- The solution describes a stationary, asymptotically NHEK geometry with a localized strut.
- Deep infrared limit yields two separate pierced-NHEK throats.
- The isometry group SL(2,R)×U(1) is preserved despite the strut.

## Abstract

We present a new vacuum solution of Einstein's equations describing the near horizon region of two neutral, extreme (zero-temperature), co-rotating, non-identical Kerr black holes. The metric is stationary, asymptotically near horizon extremal Kerr (NHEK), and contains a localized massless strut along the symmetry axis between the black holes. In the deep infrared, it flows to two separate throats which we call "pierced-NHEK" geometries: each throat is NHEK pierced by a conical singularity. We find that in spite of the presence of the strut for the pierced-NHEK geometries the isometry group SL(2,R)xU(1) is restored. We find the physical parameters and entropy.