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arXiv 1012.5111gr-qcastro-ph.GAastro-ph.HE
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黑洞附近的强迫运动

Forced motion near black holes

Jonathan R. Gair, Eanna E. Flanagan, Steve Drasco, Tanja Hinderer, Stanislav Babak

备注：
28 pages, 2 figures, submitted to Phys. Rev. D; v2 has minor changes for consistency with published version, plus a new section discussing the relative advantages of the two approaches
发表信息：
Phys.Rev.D83:044037,2011
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摘要：

我们提出了两种方法来集成强制测地线方程的克尔时空，它可以容纳任意的力。作为一个测试案例，我们在一个简单的阻力下计算吸气，模仿气体的存在。我们验证了这两种方法给出了相同的结果，这个简单的力。我们发现，阻力通常会导致离心率增加整个内旋。这是一种相对论效应，与引力辐射驱动的吸气相反，与气体双星的流体动力学模拟相似。我们通过导出对牛顿动力学的首阶相对论修正，给出了一个解析解释。如果被观测到，离心率的增加将提供明确的证据，表明内旋发生在非真空环境中。我们的两种方法是特别有用的演变轨道在绝热制度。两者都使用密切轨道的方法，其中轨道上的每个点的特征在于具有相同瞬时位置和速度的测地线的参数。这两种方法都描述了轨道的大地能量，轴向角动量，卡特常数，方位角相位，和两个角度变量，单调增加，是相对论概括的偏心异常。这两种方法在轨道相位的处理和力的表示上有所不同。在一种方法中，测地线相位和相位常数一起演化为单个轨道相位参数，并且力以其在Kinnersley正交四分体上的分量表示。在第二种方法中，测地线运动的相位常数被单独演化，力被表示为它的Boyer-Lindquist分量。这第二种方法是一个推广的早期工作的庞德和泊松平面部队在史瓦西背景。

英文摘要：

We present two methods for integrating forced geodesic equations in the Kerr spacetime, which can accommodate arbitrary forces. As a test case, we compute inspirals under a simple drag force, mimicking the presence of gas. We verify that both methods give the same results for this simple force. We find that drag generally causes eccentricity to increase throughout the inspiral. This is a relativistic effect qualitatively opposite to what is seen in gravitational-radiation-driven inspirals, and similar to what is observed in hydrodynamic simulations of gaseous binaries. We provide an analytic explanation by deriving the leading order relativistic correction to the Newtonian dynamics. If observed, an increasing eccentricity would provide clear evidence that the inspiral was occurring in a non-vacuum environment. Our two methods are especially useful for evolving orbits in the adiabatic regime. Both use the method of osculating orbits, in which each point on the orbit is characterized by the parameters of the geodesic with the same instantaneous position and velocity. Both methods describe the orbit in terms of the geodesic energy, axial angular momentum, Carter constant, azimuthal phase, and two angular variables that increase monotonically and are relativistic generalizations of the eccentric anomaly. The two methods differ in their treatment of the orbital phases and the representation of the force. In one method the geodesic phase and phase constant are evolved together as a single orbital phase parameter, and the force is expressed in terms of its components on the Kinnersley orthonormal tetrad. In the second method, the phase constants of the geodesic motion are evolved separately and the force is expressed in terms of its Boyer-Lindquist components. This second approach is a generalization of earlier work by Pound and Poisson for planar forces in a Schwarzschild background.

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