Quasi-bound states of massive scalar fields in the Kerr black-hole spacetime: Beyond the hydrogenic approximation

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• 作者：Shahar Hod^a ; ^b ; ^{shaharhod@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 刊名：Physics Letters B
• 出版年：2015
• 出版时间：7 October 2015
• 年：2015
• 卷：749
• 期：Complete
• 页码：167-171
• 全文大小：270 K

文摘

Rotating black holes can support quasi-stationary (unstable) bound-state resonances of massive scalar fields in their exterior regions. These spatially regular scalar configurations are characterized by instability timescales which are much longer than the timescale M   set by the geometric size (mass) of the central black hole. It is well-known that, in the small-mass limit 伪≡M渭鈮?$伪\equiv M渭鈮?/mo><mn>1</mn>$ (here 渭 is the mass of the scalar field), these quasi-stationary scalar resonances are characterized by the familiar hydrogenic   oscillation spectrum: ${蠅}_{\mathrm{R}}/渭=1-{伪}^2/2{\overline{n}}_0^2$, where the integer ${\overline{n}}_0(l,n;伪\to 0)=l+n+1$ is the principal quantum number of the bound-state resonance (here the integers l=1,2,3,…$l=1,2,3,\dots$ and n=0,1,2,…$n=0,1,2,\dots$ are the spheroidal harmonic index and the resonance parameter of the field mode, respectively). As it depends only on the principal resonance parameter 2c2">${\overline{n}}_0$, this small  -mass (伪鈮?$伪鈮?/mo><mn>1</mn>$) hydrogenic spectrum is obviously degenerate  . In this paper we go beyond the small-mass approximation and analyze the quasi-stationary bound-state resonances of massive scalar fields in rapidly-spinning Kerr black-hole spacetimes in the regime 伪=O(1)$伪=O(1)$. In particular, we derive the non-hydrogenic (and, in general, non  -degenerate) resonance oscillation spectrum ${蠅}_{\mathrm{R}}/渭=\sqrt{1-{(伪/\overline{n})}^2}$, where c2c9886">$\overline{n}(l,n;伪)=\sqrt{{(l+1/2)}^2-2m伪+2{伪}^2}+1/2+n$ is the generalized principal quantum number of the quasi-stationary resonances. This analytically derived formula for the characteristic oscillation frequencies of the composed black-hole-massive-scalar-field system is shown to agree with direct numerical computations of the quasi-stationary bound-state resonances.