Critical behaviors of a(2+1)-dimensional black hole with a nonlinear electrodynamics source

On the basis of a charged BTZ black hole,we add an extra term in the metric function to describe the contribution from nonlinear electrodynamics.In this way we artificially construct a(2+1)-dimensional black hole in general relativity coupled with a nonlinear electrodynamics source.The thermodynamic quantities and Smarr formula are derived.It is found that this black hole has T-S criticality like that of an RN-Ad S black hole.Further modifying the metric function,we obtain a(2+1)-dimensional black hole possessing P-V critical behaviors similar to that of van der Waals fluid.To our knowledge,this is the first example of(2+1)-dimensional black holes having this kind of critical behavior.