Black holes are usually pictured as regions from which nothing escapes, with their interiors hidden from view. But what happens beyond the horizon remains an open question. Neutron stars—the ultra-dense remnants of supernova explosions—can accumulate dark matter over billions of years, making them ideal laboratories for studying how ordinary and dark matter interact under extreme conditions.
The authors solved modified Tolman–Oppenheimer–Volkoff equations for a system consisting of a neutron star and a dark matter halo. The dark matter was described by an Einasto profile with anisotropic pressure, where the radial pressure is negative and equals minus the energy density. For baryonic matter, they used two realistic equations of state, BSk19 and SLy4. Numerical integration proceeded from the star's center to its surface, after which the stability of the solution was checked.
As the dark matter density in the halo increases, the neutron star's radius first grows and then shrinks. At critical halo parameters, the function $g_{rr}^{-1}$ changes sign outside the star's surface, forming an event horizon. Inside the horizon, the neutron star persists as a regular, non-singular structure. This phenomenon occurs for both equations of state and spans a wide parameter range. The dark matter mass is comparable to the star's mass.
The finding shows that an event horizon does not necessarily imply a singularity or the end of structure. Regular black holes could contain baryonic matter, which changes our understanding of black hole interiors. This provides a concrete example for investigating what lies beyond the horizon and could be tested by future observations.
Future work could explore the stability of such configurations under radial perturbations. It is also important to determine whether a neutron star inside a black hole can be distinguished from an ordinary Schwarzschild black hole by external signals. The dark matter model could be generalized to more realistic profiles.
These results will impact the astrophysics of compact objects and the theory of gravity, proposing a new class of solutions to Einstein's equations with dark matter.
The next step is to analyze the stability of these configurations and search for observational signatures that distinguish them from ordinary black holes.
In neutron star astrophysics, the nature of dark matter and its influence on the structure of compact objects remains an unresolved question. This work links that question to the fundamental problem of black hole interiors, offering a new bridge between the two.
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What the work does
The study constructs a model of a neutron star embedded in a dark matter halo with an Einasto profile and anisotropic pressure. The modified Tolman–Oppenheimer–Volkoff equations are solved numerically for two equations of state (BSk19 and SLy4). It is shown that for critical halo parameters, an event horizon forms outside the stellar surface, while the star itself remains regular.
Where its strength is
The strength of the work lies in a concrete, computable example of a regular black hole containing baryonic matter, providing a tangible object for testing theories of black hole interiors.
Where it could go next
Worth trying
Why this may matter
If such configurations exist in nature, they could change our understanding of the final stages of neutron star evolution and the nature of dark matter, and also provide new testable predictions for future observations.
Nearby works in our archive
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The dark matter density required to form the horizon reaches $10^{19}$ kg/m³ — billions of times denser than the center of the Sun and comparable to the density of an atomic nucleus.
The idea of massive objects inside black holes echoes Dan Simmons' novel 'Hyperion', where structures inside a singularity influence the outside world.