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Recent studies have presented the interpretation of thermodynamic enthalpyfor the mass of BTZ black holes and the corresponding Smarr formula. All theseare made in the background of three-dimensional (3D) general relativity. Inthis paper, we extend such interpretation into general 3D gravity models. It isfound that the direct extension is unfeasible and some extra conditions arerequired to preserve both the Smarr formula and the first law of black holethermodynamics. Thus, BTZ black hole thermodynamics enforces some constraintsfor general 3D gravity models, and these constraints are consistent with allprevious discussions.

Smarr formula for BTZ black holes in general three-dimensional gravity models