A new theoretical study finds that a neutron star can persist as a regular object inside a black hole that is produced by an anisotropic dark‑matter halo. The black hole in this work is “regular,” meaning it avoids the usual singularity at the center. The authors show that, for a specific range of dark‑matter halo parameters, the spacetime outside the neutron star develops an event horizon while the star itself remains a non‑singular, hydrostatic configuration inside that horizon.

The researchers built a two‑component model that treats ordinary neutron‑star matter and dark matter separately and couples them only by gravity. The dark halo is given an Einasto density profile, ρd(r)=ρ0 exp[−(r/h)1/n], and an unusual radial equation of state pr(d) = −ρd c2 (negative radial pressure). The transverse pressure is fixed by energy conservation. These ingredients feed into a modified form of the Tolman–Oppenheimer–Volkoff (TOV) equations, which determine the structure of spherical, static stars in general relativity. The equations were solved numerically with an adaptive fourth‑order Runge–Kutta method. The neutron‑star (baryonic) matter was modeled with two standard nuclear equations of state, BSk19 and SLy4, and central baryonic densities were scanned from 2.5×1017 kg/m3 up to the causality limits quoted for each equation of state (about 3.38×1018 kg/m3 for BSk19 and 3.01×1018 kg/m3 for SLy4).

At a high level the effect comes from two competing contributions of the halo. The Einasto halo adds gravitational mass outside the star and, because of the chosen equation pr(d)=−ρd c2, it also supplies a negative radial pressure. For some combinations of the halo central density ρ0, scale radius h, and Einasto index n, the metric function grr−1 (which controls whether radial distances behave normally) changes sign outside the stellar surface. That sign change signals the appearance of horizons: grr−1 stays positive inside the star, becomes negative in a shell outside it (producing an inner and outer horizon), and returns to positive far away. The paper gives concrete structural changes: for example, with h=5 km, n=1 and baryonic central density ρc=0.5×1018 kg/m3, increasing the halo central density ρ0 from 0 to 0.3×1019 kg/m3 moves the neutron‑star radius R from about 11.87 km to 10.12 km via a mild expansion then contraction.