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arXiv 1207.0504gr-qcastro-ph.HEhep-th
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高维黑洞周围的潮汐效应

Tidal effects around higher-dimensional black holes

Richard Brito, Vitor Cardoso, Paolo Pani

摘要:

在四维时空中,黑洞周围的卫星会产生低振幅的潮汐,从黑洞旋转中提取的能量总是小于损失到无穷大的引力辐射。因此,围绕黑洞旋转的卫星螺旋上升,最终合并。然而,已经证实,在高维时空中,绕轨道运行的物体会产生更强的潮汐,通过潮汐加速物体向外运动而产生反作用。这种效应类似于地月系统所经历的潮汐加速,将决定双星的演化。在这里,我们通过研究耦合到无质量标量场的物质来检验这个猜想,该场在更高维度中围绕着一个单旋转的黑洞运行。我们表明,在大于5的维度,从黑洞通过超辐射提取的能量大于进行到无穷大的能量。我们的数值结果与解析近似非常吻合,并有力地支持了在高维中潮汐加速度是规则而不是例外的猜想。超辐射支配着能量收支,卫星“外旋”;对于某些特定的轨道频率,在视界提取的能量等于发射到无穷远的能量,“浮动轨道”通常会发生。我们给出了解释这种现象的膜范式和潮汐加速由于能量耗散跨越地平线。

英文摘要:

In four-dimensional spacetime, moons around black holes generate low-amplitude tides, and the energy extracted from the hole's rotation is always smaller than the gravitational radiation lost to infinity. Thus, moons orbiting a black hole inspiral and eventually merge. However, it has been conjectured that in higher-dimensional spacetimes orbiting bodies generate much stronger tides, which backreact by tidally accelerating the body outwards. This effect, analogous to the tidal acceleration experienced by the Earth-Moon system, would determine the evolution of the binary. Here, we put this conjecture to the test, by studying matter coupled to a massless scalar field in orbit around a singly-spinning rotating black hole in higher dimensions. We show that in dimensions larger than five the energy extracted from the black hole through superradiance is larger than the energy carried out to infinity. Our numerical results are in excellent agreement with analytic approximations and lend strong support to the conjecture that tidal acceleration is the rule, rather than the exception, in higher dimensions. Superradiance dominates the energy budget and moons "outspiral"; for some particular orbital frequency, the energy extracted at the horizon equals the energy emitted to infinity and "floating orbits" generically occur. We give an interpretation of this phenomenon in terms of the membrane paradigm and of tidal acceleration due to energy dissipation across the horizon.

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