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It is well known that interpreting the cosmological constant as the pressure,the AdS black holes behave as the van der Waals thermodynamic system. In thiscase, like a phase transition from vapor to liquid in a usual van der Waalssystem, black holes also changes phases about a critical point in the $P$-$V$picture, where $P$ is the pressure and $V$ is the thermodynamic volume. Here,we give a geometrical description of this phase transition. Defining therelevant Legendre invariant thermogeometrics corresponding to the twocriticality conditions, which determine the critical values of respectivethermodynamical entities, we show that the critical point refers to thedivergence of the Ricci scalars calculated from these metrics. The similardescriptions are also provided for the other two pictures of the van der Waalslike phase transition: one is $T$-$S$ and the other one is $Y$-$X$ where $T$,$S$, $X$ and $Y$ are temperature, entropy, generalized force and generalizeddisplacement; i.e. potential corresponding to external charge, respectively.The whole discussion is very general as no specific black hole metric is beingused.

Thermogeometric description of the van der Waals like phase transition in AdS black holes