Black holes in Einstein–Gauss–Bonnet gravity with a string cloud background

We obtain a black hole solution in the Einstein–Gauss–Bonnet theory for the string cloud model in a five-dimensional spacetime. We analyze the event horizons and naked singularities. Later, we compute the Hawking temperature TH, the specific heat C, the entropy S, and the Helmholtz free energy F of the black hole. The entropy was computed using the Wald formulation. In addition, the quantum correction to the Wald's entropy is considered for the string cloud source. We mainly explore the thermodynamical global and local stability of the system with vanishing or non-vanishing cosmological constant. The global thermodynamic phase structure indicates that the Hawking–Page transition is achieved for this model. Further, we observe that there exist stable black holes with small radii and that these regions are enlarged when choosing small values of the string cloud density and of the Gauss–Bonnet parameter. Besides, the rate of evaporation for these black holes are studied, determining whether the evaporation time is finite or not. Then, we concentrate on the dynamical stability of the system, studying the effective potential for s-waves propagating on the string cloud background.