We construct spontaneously vectorized black holes where a real vector field is coupled to the Gauss-Bonnet invariant. We employ three coupling functions for the vector field, and determine the respective domains of existence of the vectorized black holes. These domains of existence are bounded by the marginally stable Schwarzschild black holes and the critical vectorized black holes. We also address the effects of a mass term. For a given black hole mass the horizon radius is smaller for the vectorized black holes than for the Schwarzschild black holes. Since the vector field vanishes at the horizon, there is no contribution from the Gauss-Bonnet term to the entropy of the vectorized black holes.

我们构造自发向量化的黑洞，其中将实际向量场耦合到高斯-邦纳特不变式。我们对矢量场采用三个耦合函数，并确定矢量化黑洞存在的各个域。这些存在域由边界稳定的Schwarzschild黑洞和临界矢量化黑洞限制。我们还讨论了质量术语的影响。对于给定的黑洞质量，矢量化黑洞的视界半径小于Schwarzschild黑洞的视界半径。由于矢量场在地平线上消失，因此高斯-邦纳特项对矢量化黑洞的熵没有贡献。