Center for Radiophysics and Space Research, Cornell University, Ithaca, New York 14853, USA.
Phys Rev Lett. 2012 Aug 17;109(7):071102. doi: 10.1103/PhysRevLett.109.071102. Epub 2012 Aug 15.
We show that transient resonances occur in the two-body problem in general relativity for spinning black holes in close proximity to one another when one black hole is much more massive than the other. These resonances occur when the ratio of polar and radial orbital frequencies, which is slowly evolving under the influence of gravitational radiation reaction, passes through a low order rational number. At such points, the adiabatic approximation to the orbital evolution breaks down, and there is a brief but order unity correction to the inspiral rate. The resonances cause a perturbation to orbital phase of order a few tens of cycles for mass ratios ∼10(-6), make orbits more sensitive to changes in initial data (though not quite chaotic), and are genuine nonperturbative effects that are not seen at any order in a standard post-Newtonian expansion. Our results apply to an important potential source of gravitational waves, the gradual inspiral of white dwarfs, neutron stars, or black holes into much more massive black holes. Resonances' effects will increase the computational challenge of accurately modeling these sources.
我们表明，当两个彼此靠近的旋转黑洞中一个的质量远远超过另一个时，广义相对论中的双体问题会出现瞬态共振。当极向和径向轨道频率之比在引力辐射反应的影响下缓慢演化，并通过低阶有理数时，就会发生这些共振。在这些点上，轨道演化的绝热近似失效，并且对进动率有一个短暂但数量级为 1 的修正。共振使质量比约为 10(-6)的轨道相位产生几十圈的微扰，使轨道对初始数据的变化更加敏感（尽管不是完全混沌），并且是真实的非微扰效应，在标准的后牛顿展开的任何阶次都不会出现。我们的结果适用于引力波的一个重要潜在源，即白矮星、中子星或黑洞逐渐进入质量更大的黑洞的过程。共振的影响将增加准确模拟这些源的计算挑战。
