In this paper, we derive a novel Schwarzschild-like black hole (BH) solution describing a static and asymptotically flat BH surrounded by a dark matter (DM) halo with a Dehnen-type density distribution in the surrounding environment. We investigate the properties of the obtained BH by studying the curvature properties and energy conditions in Einstein gravity. Furthermore, we explore the features of a novel Schwarzschild-like BH embedded in a DM halo with Dehnen-type density profile by analyzing the timelike geodesics of particles along with BH observable properties.

In this paper, we investigate the thermodynamics and phase transitions of asymptotically anti-de Sitter black holes (BHs) in the presence of ModMax nonlinear electrodynamics (NLED) and perfect fluid dark matter (PFDM). Combining the effects of ModMax theory, characterized by the nonlinearity parameter $$\gamma $$ γ , and PFDM, described by the parameter $$\alpha $$ α , we derive an exact solution for the BH metric and analyze its thermodynamic properties. We explore the critical behavior of the BHs by studying the Hawking temperature, heat capacity, and Gibbs free energy. The results demonstrate the existence of phase transitions analogous to those found in van der Waals fluids, with the ModMax parameter and dark matter playing crucial roles in modifying the critical points and stability of the BH. In addition, we employ geometric thermodynamic methods (GTM), including the Weinhold, Ruppeiner, and HPEM metrics, to further examine the stability and phase structure of BHs. Our study provides new insights into how NLED and dark matter are interrelated within BH thermodynamics.

By considering the concept of the modified Chaplygin gas (MCG) as a single fluid model unifying dark energy and dark matter, we construct a static, spherically charged black hole (BH) solution in the framework of General Relativity. The P–V criticality of the charged anti-de Sitter (AdS) BH with a surrounding MCG is explored in the context of the extended phase space, where the negative cosmological constant operates as a thermodynamical pressure. This critical behavior shows that the small/large BH phase transition is analogous to the van der Waals liquid/gas phase transition. Accordingly, along the P–V phase spaces, we derive the BH equations of state and then numerically evaluate the corresponding critical quantities. Similarly, critical exponents are identified, along with outcomes demonstrating the scaling behavior of thermodynamic quantities near criticality to a universal class. The use of geometrothermodynamic (GT) tools finally offers a new perspective on the discovery of the critical phase transition point. At this stage, we apply a class of GT tools, such as Weinhold, Ruppeiner, HPEM, and Quevedo classes I and II. The findings are therefore non-trivial, as each GT class metric captures at least either the physical limitation point or the phase transition critical point. Overall, this paper provides a detailed study of the critical behavior of the charged AdS BH with surrounding MCG.

Kalb-Ramond (KR) gravity is an intriguing model incorporating local Lorentz violation, and black hole (BH) solutions are known to exist. In this study, we investigate some crucial aspects of BHs endowed with a global monopole charge in the self-interacting KR field. Specifically, we study the quasinormal modes (QNMs) corresponding to scalar, electromagnetic, and gravitational perturbations; derive rigorous bounds for the greybody factors (GBFs); and examine the sparsity of Hawking radiation. The effects of the model parameters ℓ (Lorentz-violating parameter in KR gravity) and η (monopole charge) on these phenomena are elaborated. First, QNMs are evaluated with high precision using the 13 ^th -order Padé-averaged WKB method and cross-examined via time-domain analyses within an acceptable parameter space. The results show that the estimated QNMs are more sensitive to ℓ; however, both model parameters influence the frequency spectra. The derived bounds on the GBFs aid in further constraining the parameter space. It is shown that ℓ and η have a similar effect on the greybody bounds. Furthermore, positive and negative values of ℓ have opposing effects in that the bounds are reversed for the two cases. The analyses of the Hawking radiation sparsity highlight the effect of ℓ, and two scenarios are noted: either the radiation emitted is less sparse than Hawking radiation, or it is sparser during the evaporation phase. Thus, this work presents a comprehensive account of BHs in KR gravity with a global monopole charge.