Yu-Qian Zhao | Searcharxiv

arXiv2026

Quasinormal modes and tidal responses of black holes in generic anisotropic matter environments

We develop a perturbative framework for a black hole embedded in a generic, possibly anisotropic, matter environment under spherical symmetry. Our approach extends previous analyses restricted to vanishing radial pressure or to perturbative matter configurations. Within this framework, we derive an analytical generalization of the Einstein cluster that incorporates a polytropic radial pressure, and we investigate the properties of this solution. We show that both the geodesic structure and the axial quasinormal-mode spectrum remain predominantly governed by an overall gravitational redshift effect, while the radial pressure systematically enhances the environmental corrections. In contrast, the tidal Love numbers are substantially more sensitive, and can exhibit order-unity deviations, including vanishing and negative strictly static magnetic Love numbers for sufficiently large anisotropy. We present the full linearized equations, which can be applied to various extensions, including ringdown analysis and extreme-mass-ratio inspirals.

gr-qc↗

arXiv2026

A metric solution for rotating black holes embedded in dark matter halos with central spikes

We propose an analytic metric describing rotating black holes surrounded by generic dark matter halos. This metric is an exact solution of the field equations that incorporates a dark matter halo with a central density spike in the vicinity of the black hole. Following the construction of the corresponding spherically symmetric solution proposed by Cardoso {\it et al.}, the rotating geometry is seeded by a mass function characterizing the dark matter distribution surrounding the black hole. The dark matter profile is truncated at a radius close to the horizon, in accordance with analyses based on adiabatic invariants, so that the energy density as well as the radial and tangential pressures vanish identically beyond this point. The presence of the spike and the associated metric discontinuity implies that the dark matter is locally anisotropic. The resulting geometry is asymptotically flat and reduces to several well-known cases under suitable limits. In particular, it generalizes the corresponding spherically symmetric solution to the case of rotating black holes. We discuss the physical interpretation of the model parameters and illustrate the metric by applying it to several specific gravitational systems.

gr-qc↗