Abdelghani Errehymy

The Event Horizon Telescope (EHT) has provided images of the supermassive black holes Sgr A* and M87*, enabling direct tests of gravity. Any extended mass distribution, such as a dark matter halo, perturbs null geodesics in the photon-ring regime, making shadow measurements a probe of inner-halo structure. In this work, we investigate static, spherically symmetric black holes surrounded by Einasto-type dark matter halos and derive constraints from EHT shadow data. Starting from the Einasto density profile with parameters ϱ 0 , α ˜ , ν ˜ , we construct a metric function f ( r ) = 1 − 2 M / r + 2 M ∞ g ˜ ( r ) that interpolates between the black hole horizon and the asymptotic halo, following the approach of Xu et al. but adapted specifically to the Einasto scenario. We analyze the photon potential, null geodesics, and shadow radius as functions of black hole mass M in the nonspinning limit. Using the dimensionless shadow diameter d _sh ≡ Dθ / M measured by the EHT— d sh M 87 * = 11.0 ± 1.5 and d sh Sgr A * = 9.5 ± 1.4 —we perform Bayesian parameter estimation to identify allowed regions in the Einasto parameter space. Combined with the independently measured black hole masses from stellar dynamics, our results place constraints on the inner dark matter distribution: for Sgr A*, adopting the stellar-orbit mass prior, we find ϱ ₀ ≲ 10 ⁻¹¹ M _⊙ pc ⁻³ at 1 σ confidence, while for M87*, the bounds are weaker due to distance uncertainties. The Einasto index ν ˜ is weakly constrained, indicating that EHT precision primarily limits the mass enclosed near the photon sphere rather than the profile slope. These findings demonstrate that horizon-scale imaging can complement galactic-scale dynamics in probing dark matter models, including fuzzy dark matter scenarios with solitonic cores. Future EHT observations will refine these constraints and distinguish between competing dark matter descriptions.

This work investigates slowly rotating traversable wormholes supported by string fluids whose properties vary with distance from the throat. This radial variation allows the matter to transition smoothly from a de Sitter‐like core near the center to a string‐dominated environment further out, producing a regular, horizon‐free, and asymptotically flat spacetime. By allowing the transverse pressure to depend on radius, the fluid adapts naturally to the surrounding geometry, yielding a well‐behaved energy density and shape function. Even modest rotation introduces frame‐dragging effects that twist photon paths, creating differences between co‐rotating and counter‐rotating trajectories. These effects are strongest near the throat, while at larger distances the spacetime is largely governed by the static gravitational field. Circular photon orbits reveal that the interplay of the redshift function, wormhole shape, and rotation determines the photon‐sphere structure. Different radial profiles of the string fluid generate distinctive photon‐ring patterns, providing potential observational signatures of both rotation and the internal matter distribution. Overall, radially varying string fluids provide a flexible and physically consistent source for traversable wormholes, bridging vacuum‐like and string‐dominated regions while maintaining regularity and supporting slow‐rotation. This study highlights how anisotropic matter influences curvature and light propagation, offering a realistic framework for horizonless exotic spacetimes.