In the present paper we study the onset of the spin-induced scalarization of a Kerr black hole in scalar-Gauss–Bonnet gravity with a massive scalar field. Our approach is based on a \((2+1)\) time evolution of the relevant linearized scalar field perturbation equation. We examine the region where the Kerr black hole becomes unstable giving rise to new scalarized rotating black holes with a massive scalar field. With increasing of the scalar field mass, the minimum value of the Gauss–Bonnet coupling parameter at which scalarization is possible, increases and thus the instability region shrinks. Interestingly, the introduction of scalar field mass does not change the critical minimal value of the black hole angular momentum \(a_{\mathrm{crit}}/M\) where the instability of the Kerr black hole develops.

在本文中，我们研究了自旋诱导的标量高斯标量的标量-高斯-贝内特引力中Kerr黑洞的标量化的开始。我们的方法基于相关线性化标量场摄动方程的（（2 + 1）\）时间演化。我们检查了Kerr黑洞变得不稳定的区域，从而产生了具有大标量场的新的标量旋转黑洞。随着标量场质量的增加，可能进行标量的高斯-贝纳特耦合参数的最小值增加，因此不稳定区域缩小。有趣的是，引入标量场质量并不会改变黑洞角动量\（a _ {\ mathrm {crit}} / M \）的临界最小值。 克尔（Kerr）黑洞不稳定的地方发展。