Gauss-Bonnet solution with a cloud of strings in de Sitter and anti-de Sitter space

In this study,we investigate exact spherically symmetric Gauss-Bonnet black hole solutions surrounded by a cloud of string fluid with the cosmological constant in D> 4 dimensions.Both charged and uncharged cases are considered.We focus on the de Sitter solutions in the main text and provide the anti-de Sitter solutions in the appendix.We analyze the features of event horizons and thermodynamic properties of the black hole solutions.The mass,Hawking temperature,thermal stability,and phase transitions are discussed.Moreover,the equation of state and critical phenomena associated with these solutions are explored.