毛状克尔黑洞的强场引力透镜效应

Shafqat Ul Islam, Sushant G. Ghosh
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引用次数: 14

摘要

最近,由于事件视界望远镜(EHT)的结果,人们对黑洞的强引力透镜产生了浓厚的兴趣,并建议将广义相对论和修正引力理论中的黑洞透镜进行比较。这可能有助于我们评估这些模型之间的现象学差异。克尔黑洞也是一些替代引力理论的解决方案,而最近获得的修正克尔黑洞(毛茸茸的克尔黑洞)逃避了无毛定理,这是由于周围流体的额外来源,如暗物质,具有守恒的能量动量张量(EMT)。这些毛茸茸的克尔黑洞可能是另一种引力理论的解。在毛状Kerr黑洞的强偏转极限下,我们推广了前人关于Kerr黑洞引力透镜效应的研究成果,偏差参数为$\alpha$,主毛为$\ell_0$。有趣的是,挠度系数$\bar{a}$分别随着$\ell_0$和$\alpha$的增大而增大和减小。$\bar{b}$与$\ell_0$和$\alpha$表现出相反的行为。挠度角$\alpha_D$、角位置$\theta_{\infty}$和$u_{m}$减小,角间距$s$随$\alpha$增大。我们将我们的结果与Kerr黑洞的结果进行了比较,并应用该形式化理论讨论了超大质量黑洞Sgr A*和M87*的天体物理结果。我们观察到,Sgr A*与Kerr黑洞的角位置偏差不超过$2.6~\mu$, M87*与Kerr黑洞的角位置偏差不超过$1.96~\mu$,这是目前EHT观测无法解决的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Strong field gravitational lensing by hairy Kerr black holes
The recent time witnessed a surge of interest in strong gravitational lensing by black holes due to the Event Horizon Telescope (EHT) results, suggesting comparing the black hole lensing in general relativity and modified gravity theories. That may help us to assess the phenomenological differences between these models. A Kerr black hole is also a solution to some alternative theories of gravity, while recently obtained modified Kerr black holes (hairy Kerr black holes), which evade the no-hair theorem, are due to additional sources the surrounding fluid, like dark matter, having conserved energy momentum tensor (EMT). These hairy Kerr black holes may be solutions to an alternative theory of gravity. We generalize previous work on gravitational lensing by a Kerr black hole, in the strong deflection limits to the hairy Kerr black holes, with deviation parameter $\alpha$ and a primary hair $\ell_0$. Interestingly, the deflection coefficient $\bar{a}$, respectively, increases and decreases with increasing $\ell_0$ and $\alpha$. $\bar{b}$ shows opposite behaviour with $\ell_0$ and $\alpha$. We also find that the deflection angle $\alpha_D$, angular position $\theta_{\infty}$ and $u_{m}$ decreases, but angular separation $s$ increases with $\alpha$. We compare our results with those for Kerr black holes, and also, the formalism is applied to discuss the astrophysical consequences in the context of the supermassive black holes Sgr A* and M87*. We observe that the deviations of the angular positions from that of the Kerr black hole are not more than $2.6~\mu$as for Sgr A* and $1.96~\mu$as for M87*, which are unlikely to get resolved by the current EHT observations.
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