Some remarks on Hayward-AdS black hole surrounded by a fluid of strings

We obtain a class of solutions corresponding to a generalization of the Hayward black hole by solving the Einstein equations coupled to a particular nonlinear electromagnetic field. The generalization is realized by considering, additionally, the presence of the cosmological constant and a source corresponding to an anisotropic fluid, namely, a fluid of strings, that surrounds the black hole. We show that the obtained class of solutions preserves or does not the regularity of the original Hayward black hole solution, depending on the values of the parameter $\beta$ which labels the different solutions. We discuss the characteristics of the solutions, from the point of view of the singularities of spacetime, by examining the behavior of the Kretschmann scalar as well as of the geodesics concerning their completeness. We analyze some aspects of thermodynamics, particularizing one of the solutions obtained, namely, for $\beta =-1/2$, in which case the regularity of the Hayward black hole is preserved. Some thermodynamic quantities are obtained and analyzed, for example, pressure, heat capacity, and the critical points, and we show how these quantities change for different values of the parameter $q$ associated with the original Hayward solution, as well as with the parameter $b$ associated with the presence of the fluid of strings. The phase transitions are also analyzed by using the equation of state and the Gibbs free energy.