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arXiv 1807.06263gr-qc
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Kerr-Newman时空中质量标量场的不稳定性

On the instability for massive scalar fields in Kerr-Newman spacetime

Yang Huang, Dao-Jun Liu, Xiang-hua Zhai, Xin-zhou Li

摘要:

在Kerr-Newman黑洞的背景中,一个大质量的带电标量场可以引发超辐射不稳定性。在本文中,我们提出了一个数值研究,这样的不稳定性使用连分式方法。结果表明,对于给定的黑洞,具有特定方位角指数$m$的不稳定标量模只出现在标量场参数空间的有限区域内。标量云的最大质量正好是不稳定模质量的上界。我们证明了由于标量场与Kerr-Newman黑洞之间的电磁相互作用,在相同转动参数的Kerr时空中,不稳定性的增长率可以比标量场的增长率大$15.7\%$.此外,我们还发现了一个增长率的最大值$τ^{-1}=1.788\times 10^{-7}M^{-1}$,它比Kerr情形下的增长率大$4\%$.

英文摘要:

It is known that a massive charged scalar field can trigger a superradiant instability in the background of a Kerr-Newman black hole. In this paper, we present a numerical study of such an instability by using the continued fraction method. It is shown that for given a black hole, the unstable scalar mode with a specific azimuthal index $m$ only occurs in a finite region in the parameter space of the scalar field. The maximum mass of the scalar cloud is exactly the upper bound of the mass of the unstable modes. We show that due to the electromagnetic interaction between the scalar field and the Kerr-Newman black hole, the growth rate of the instability can be $15.7\%$ larger than that of a scalar field in Kerr spacetime of the same rotation parameter. In addition, we find a maximum value of the growth rate $τ^{-1}=1.788\times 10^{-7}M^{-1}$, which is about $4\%$ larger than that in the Kerr case.

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