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.
Categories: gr-qc hep-th