On the absence of inner horizons for anisotropic black holes

Abstract We establish a general no-inner horizon theorem for a wide class of static anisotropic black holes in Einstein gravity. Working in an orthonormal frame, we show that anisotropic scaling inevitably induces a non-vanishing “effective pressure difference” between spatial directions apart from the radial direction. We prove that, provided this effective pressure difference satisfies a simple integral condition which holds in a general setting, inner (Cauchy) horizons are excluded. As an application, we demonstrate that a large variety of black holes which possess homogeneous but anisotropic three-dimensional horizons can not have inner horizons. These anisotropic horizon geometries fall within various Bianchi types. As a specific example, we investigate the internal structure of a charged black hole solution with a Bianchi type II horizon by combining analytical and numerical methods, and we find the absence of the inner horizon and a stable Kasner universe near the spacelike singularity. Our theorem is consistent with some previously known results, implying an underlying mechanism that certain kinds of spatial anisotropy can remove inner horizons. Consequently, anisotropic black holes generically develop spacelike singularities in their interiors, offering new insight into the interplay between anisotropy, strong cosmic censorship, and black hole interior structures.