In singular limits where both the temperature and horizon area of black holes can be tuned to zero, while keeping the area-over-temperature–ratio fixed, singular near-horizon geometries can be constructed. Such singular near-horizon geometries contain a local AdS3 factor, which can be either a null self-dual orbifold or a pinching orbifold, as noted in [33Jump To The Next Citation Point, 29, 135, 23Jump To The Next Citation Point] (see [116Jump To The Next Citation Point] for a comprehensive study of the simplest three-dimensional model and [243Jump To The Next Citation Point] for a partial classification of four-dimensional vanishing area near-horizon solutions of (1View Equation)).