In the realm of astrophysics, black holes exist within nonvacuum cosmological backgrounds, making it crucial to investigate how these backgrounds influence the properties of black holes. In this work, we first introduce a novel static spherically-symmetric exact solution of Einstein field equations representing a surrounded hairy black hole. This solution represents a generalization of the hairy Schwarzschild solution recently derived using the extended gravitational decoupling method. Then, we discuss how the new induced modification terms attributed to the primary hairs and various background fields affect the geodesic motion in comparison to the conventional Schwarzschild case. Although these modifications may appear insignificant in most cases, we identify specific conditions where they can be comparable to the Schwarzschild case for some particular background fields.

In this paper, we apply the gravitational decoupling method for dynamical systems in order to obtain a new type of solution that can describe a hairy dynamical black hole. We consider three cases of decoupling. The first one is the simplest and most well known when the mass function is the function only of space coordinate r. The second case is a Vaidya spacetime case when the mass function depends on time v. Finally, the third case represents the generalization of these two cases: the mass function is the function of both r and v. We also calculate the apparent horizon and singularity locations for all three cases.

In this paper, we consider using the gravitational decoupling method to obtain a hairy regular black hole which corresponds to the Hayward model. We modify the hairy Schwarzschild solution to obtain the regular Kretschmann scalar. The energy momentum of a new model is considered, and we show that there is an energy exchange between its parts.

A thermodynamic model of the ternary fluid system H₂O–LiCl–NaCl is proposed for the temperature range from –77 to +300°C. This model incorporates low-temperature phase transitions of freezing products of water–salt inclusions. The model is based on the Pitzer equations using new interaction parameters of Na, Cl, and the corresponding equilibrium constants of reactions involving the solid and liquid phases. Based on microthermometry data of fluid inclusions (T of phase transitions during heating after freezing), the model allows determination of the salt concentrations. The characteristics (T, wt %, LiCl and NaCl) of triple points with solid phases including the eutectic \({\text{E}}{\kern 1pt} ''\) (ice + LiCl · 5H₂O + NaCl · 2H₂O), peritectic \({\text{P}}_{1}^{{{\text{''}}}}\) (LiCl · 5H₂O + NaCl · 2H₂O + NaCl) and \({\text{P}}_{2}^{{{\text{''}}}}\) (LiCl · 5H₂O + LiCl · 3H₂O + NaCl), and the cotectic, peritectic curves separating the phase fields (ice + L, NaCl · 2H₂O + L, NaCl + L), as well as solubility isotherms of ice, hydrohalite, and halite calculated by the model, showed good agreement with the experimental data. As an example of the application of a model to a natural object, we determined the salt contents in lithium-bearing brine inclusions in late quartz veins of the Bolshie Keivy area (Fennoscandian Shield).