Hayward–Letelier Black Holes in AdS Spacetime

We analyze Hayward black holes (BHs) with a negative cosmological constant surrounded by a cloud of strings, which we designate Hayward–Letelier AdS BHs. These solutions can be obtained by coupling the Einstein equations with nonlinear electrodynamics and the energy–momentum tensor of clouds of strings. We show that these solutions are no longer regular and have a curvature singularity at the center. In turn, we analyze the thermodynamics associated with these BHs by establishing the form of the Smarr formula and the first law of thermodynamics. We derive the expressions for the thermodynamic quantities such as pressure, temperature, heat capacity, Gibbs free energy, and isothermal compressibility. We explore the phase structure of these solutions by analyzing the behavior of the heat capacity and Gibbs free energy. These solutions exhibit a first-order phase transition, similar to van der Waals fluids. We also check the behavior of the thermodynamic quantities near the critical points and calculate the values of the critical exponents. This illustrates a robust analogy between our solutions and van der Waals fluids.