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-AdS 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.

中文翻译：

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具有非线性电动力学源的（2 +1）维黑洞的临界行为

在带电的BTZ黑洞的基础上，我们在度量函数中添加了一个附加项来描述非线性电动力学的作用。通过这种方式，我们在广义相对论中人工构造了一个（2 +1）维黑洞，并耦合了非线性电动力源。推导了热力学量和Smarr公式。发现该黑洞具有与RN-AdS黑洞相同的TS临界。进一步修改度量函数，我们获得一个（2 +1）维黑洞，该黑洞具有类似于Van der Waals流体的P-V临界行为。据我们所知，这是具有这种临界行为的（2 + 1）维黑洞的第一个示例。