Bound orbits of a slowly evolving black hole
Bound orbits of a slowly evolving black hole
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DOI：
10.1103/physrevd.100.064001
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发表时间：
2018-06
影响因子：
5
通讯作者：
S. Hughes
中科院分区：
文献类型：
--
作者：
S. Hughes
黑洞的束缚轨道已经被很好地理解了。给定一个质量为$M$，自旋为$S = aM^2$的克尔黑洞，很容易将其轨道描述为轨道几何形状的函数。如果黑洞本身也在演化，轨道会如何变化？如果绕轨道运行的物体进化，轨道是如何变化的？在本文中，我们考虑了一个改变黑洞质量和自旋的过程，使时空在任何时刻都由克尔解描述，或者改变轨道物体的质量。如果这种变化发生缓慢，轨道的运动（$J_r, J_\theta, J_\phi$）是{\it绝热不变量，因此}在这个过程中是恒定的。通过强化这些作用的绝热不变性，我们推断出轨道是如何随着黑洞质量、自旋和轨道体质量的变化而演变的。我们用几个例子来证明这些结果的影响：如果吸积改变了黑洞的质量和自旋，轨道是如何反应的；如果轨道天体的质量因吸积而发生变化，它会如何反应；以及小天体进入黑洞的灵感如何受到黑洞质量和自旋变化的影响，这是由于事件视界吸收的引力辐射造成的。在所有情况下，影响都非常小，但可能比以前的工作中发现的要大一个数量级或更大，因为以前的工作没有考虑到轨道对这些影响的反应。
Bound orbits of black holes are very well understood. Given a Kerr black hole of mass $M$ and spin $S = aM^2$, it is simple to characterize its orbits as functions of the orbit's geometry. How do the orbits change if the black hole is itself evolving? How do the orbits change if the orbiting body evolves? In this paper, we consider a process that changes a black hole's mass and spin, acting such that the spacetime is described by the Kerr solution at any moment, or that changes the orbiting body's mass. Provided this change happens slowly, the orbit's actions ($J_r, J_\theta, J_\phi$) are {\it adiabatic invariants}, and thus are constant during this process. By enforcing adiabatic invariance of the actions, we deduce how an orbit evolves due to changes in the black hole's mass and spin and in the orbiting body's mass. We demonstrate the impact of these results with several examples: how an orbit responds if accretion changes a black hole's mass and spin; how it responds if the orbiting body's mass changes due to accretion; and how the inspiral of a small body into a black hole is affected by change to the hole's mass and spin due to the gravitational radiation absorbed by the event horizon. In all cases, the effect is very small, but can be an order of magnitude or more larger than what was found in previous work which did not take into account how the orbit responds due to these effects.