Thermodynamics of 4D dS/AdS Gauss-Bonnet black holes from consistent gravity theory in presence of cloud of strings

By looking at the Lovelock theorem one can infer that the gravity model given by \cite{GL} could not applicable for all type of 4D Einstein Gauss Bonnet (GB) curved spacetimes. Because in 4D space time the Gauss-Bonnet invariant is a total derivative, and hence it does not contribute to the gravitational dynamics. Hence, authors in the work \cite{AL} presented an alternative consistent EGB gravity model instead of \cite{GL} by applying break of diffeomorphism property. In this work we use it to produce a dS/AdS black hole metric and then investigate its thermodynamic behavior in presence of cloud of Numbo Goto strings.