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Dynamics and relativistic tests of Schwarzschild black holes in Dehnen dark matter halos
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DOI：10.1016/j.dark.2026.102393.png)
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Abstract
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In this paper, we selected a phenomenological model of a static, spherically symmetric black hole immersed in a Dehnen-(1,4,γ) type dark matter halo. To systematically probe how different dark matter central-density behaviors (centrally depleted, cored, cuspy) affect the dynamics and relativistic observables in the vicinity of a black hole, we selected three distinct values: γ=−1, 0, and 1, respectively. Our analysis of the radii of characteristic circular orbits and shadows reveals that the presence of dark matter significantly enhances the gravitational attraction of the black hole. In addition to obtaining exact solutions, we derive analytical expressions for relevant physical quantities within the small characteristic mass of the core of the dark matter halo compared to the black hole mass approximation, which corresponds well to ultracompact dwarf galaxies and locally black hole dominated systems, where dark matter’s effect on stellar orbits is small. Notably, we introduce a common factor associated with the γ parameter that quantifies the dark matter contribution relative to the Schwarzschild spacetime. Furthermore, by analyzing gravitational lensing and Shapiro time delay in the weak-field regime and comparing it with data from relativistic tests in the Solar System, we place conservative upper bounds on the dark matter core mass parameter as a small correction to the Schwarzschild metric. For representative values of γ, where the dimensionless factor a(γ) is of order unity, the strongest weak-field bound is of order Ms/M≲10−5. These Solar System bounds are model-dependent consistency limits on effective Schwarzschild-deviation terms and should not be interpreted as direct evidence for a Dehnen halo around the Sun. Moreover, by analyzing the quasinormal modes of perturbations of these black holes in the eikonal regime, we found that embedding a Schwarzschild black hole in a dark matter environment leads to a decrease in the oscillation frequency and an increase in the relaxation time of the perturbations compared to the isolated Schwarzschild black hole.
Keywords:
Black hole
Dehnen dark matter
Solar System tests
Circular orbits
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