We test the validity of the weak cosmic censorship conjecture for the ($2+1$)-dimensional charged anti-de Sitter black hole solution, which was derived by Martinez, Teitelboim, and Zanelli (MTZ). We first construct a thought experiment by throwing test charged particles on an extremal MTZ black hole. We derive that extremal ($2+1$) dimensional black holes can be overcharged by test particles, unlike their analogues in $4$ and higher dimensions. Nearly-extremal black holes can also be overcharged, by a judicious choice of energy and charge for the test particles in the case when we ignore the second order effects. Contrary to this, nearly-extremal black holes cannot be overcharged by the second order perturbation, obeying the weak cosmic censorship conjecture.

中文翻译：

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测试极值和近极值 (2+1) 维 MTZ 黑洞的宇宙审查猜想

我们测试了由 Martinez、Teitelboim 和 Zanelli (MTZ) 推导出的 ($2+1$) 维带电反德西特黑洞解的弱宇宙审查猜想的有效性。我们首先通过在极值 MTZ 黑洞上投掷测试带电粒子来构建一个思想实验。我们推导出极值 ($2+1$) 维度黑洞可以被测试粒子过度充电，这与它们在 $4$ 和更高维度中的类似物不同。在我们忽略二阶效应的情况下，通过明智地选择测试粒子的能量和电荷，接近极值的黑洞也可能被过度充电。与此相反，接近极值的黑洞不能被二阶扰动过度充电，遵守弱宇宙审查猜想。