膜世界Kerr黑洞圆盘的轨道共振
Orbital resonances in discs around braneworld Kerr black holes
摘要：
Randall-Sundrum型brany宇宙中的旋转黑洞用Kerr几何来描述，其中潮汐荷b代表brany黑洞与体时空的相互作用。B1<0 rotating black holes with dimensionless spin a>是允许的。研究了潮汐荷b在黑洞系统QPO轨道共振模型中的作用。给出了赤道、准圆大地运动的轨道开普勒、径向和垂直周转频率，并讨论了它们的径向轮廓。共振条件给出了在三个天体物理相关的情况下：直接（参数）共振，相对论性进动模型，并为一些被困振荡的翘曲盘，共振组合频率。它示出，如何b可以影响匹配的观测数据表明3：2的频率比观察到的GRS 1915+105微类星体的轨道共振模型的预测;限制允许范围内的黑洞参数a和b的建立。在半径为ν_K：ν_θ：ν_r=3：2：1的情况下，能产生强共振现象的“神奇”无量纲黑洞自旋取决于b。即使在具有高度散射的共振频率的源中，这种强共振也可能是相关的，如在Sgr A* 中所预期的。当存在比半径时，给出了a和b的具体值，其中v_K：v_θ：v_r=s：t：u，其中5>=s>t>u为小自然数。结果表明，对于某些比值，这种情况在黑洞场中是不可能的。在轨道共振模型的框架下分析微类星体的高频QPO，可以对brany Kerr黑洞的潮汐荷提出相应的限制。
英文摘要：
Rotating black holes in the brany universe of the Randall-Sundrum type are described by the Kerr geometry with a tidal charge b representing the interaction of the brany black hole and the bulk spacetime. For b<0 rotating black holes with dimensionless spin a>1 are allowed. We investigate the role of the tidal charge b in the orbital resonance model of QPOs in black hole systems. The orbital Keplerian, the radial and vertical epicyclic frequencies of the equatorial, quasicircular geodetical motion are given and their radial profiles are discussed. The resonant conditions are given in three astrophysically relevant situations: for direct (parametric) resonances, for the relativistic precession model, and for some trapped oscillations of the warped discs, with resonant combinational frequencies. It is shown, how b could influence matching of the observational data indicating the 3:2 frequency ratio observed in GRS 1915+105 microquasar with prediction of the orbital resonance model; limits on allowed range of the black hole parameters a and b are established. The "magic" dimensionless black hole spin enabling presence of strong resonant phenomena at the radius where ν_K:ν_θ:ν_r=3:2:1 is determined in dependence on b. Such strong resonances could be relevant even in sources with highly scattered resonant frequencies, as those expected in Sgr A*. The specific values of a and b are given also for existence of specific radius where ν_K:ν_θ:ν_r=s:t:u with 5>=s>t>u being small natural numbers. It is shown that for some ratios such situation is impossible in the field of black holes. We can conclude that analysing the microquasars high-frequency QPOs in the framework of orbital resonance models, we can put relevant limits on the tidal charge of brany Kerr black holes.
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