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Thermodynamic geometry is applied to the Born-Infeld-anti-de Sitter blackhole (BIAdS) in the four dimensions, which is a nonlinear generalization of theReissner-Norstr\"Aom-AdS black hole (RNAdS). We compute the Weinhold as well asthe Ruppeiner scalar curvature and find that the singular points are not thesame with the ones obtained using the heat capacity. Legendre-invariant metricproposed by Quevedo and the metric obtained by using the free energy as thethermodynamic potential are obtained and the corresponding scalar curvaturesdiverge at the Davies points.

Thermodynamic Geometry of the Born-Infeld-anti-de Sitter black holes