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By looking at the Lovelock theorem one can infer that the gravity model givenby \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 atotal derivative, and hence it does not contribute to the gravitationaldynamics. Hence, authors in the work \cite{AL} presented an alternativeconsistent EGB gravity model instead of \cite{GL} by applying break ofdiffeomorphism property. In this work we use it to produce a dS/AdS black holemetric and then investigate its thermodynamic behavior in presence of cloud ofNumbo Goto strings.

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