In this brief report, we investigate the existence of 4-dimensional static spherically symmetric black holes (BHs) in the Einstein-complex-scalar-Gauss-Bonnet (EcsGB) gravity with an arbitrary potential $V(\phi)$ and a coupling $f(\phi)$ between the scalar field $\phi$ and the Gauss-Bonnet (GB) term. We find that static regular BH solutions with complex scalar hairs do not exist. This conclusion does not depend on the coupling between the GB term and the scalar field, nor on the scalar potential $V(\phi)$ and the presence of a cosmological constant $\Lambda$ (which can be either positive or negative), as longer as the scalar field remains complex and is regular across the horizon.

中文翻译：

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在爱因斯坦复标量高斯博内引力中没有静态规则黑洞

在这份简短的报告中，我们研究了爱因斯坦复标量高斯博内 (EcsGB) 引力中 4 维静态球对称黑洞 (BHs) 的存在，该引力具有任意势 $V(\phi)$ 和耦合标量场 $\phi$ 和 Gauss-Bonnet (GB) 项之间的 $f(\phi)$。我们发现不存在具有复杂标量毛的静态常规 BH 解决方案。这个结论不取决于GB项和标量场之间的耦合，也不取决于标量势$V(\phi)$和宇宙常数$\Lambda$的存在（可以是正的也可以是负的），只要标量场保持复杂并且在地平线上是规则的。