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arXiv 1102.3316gr-qcastro-ph.HEhep-th
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两个一般测地线粒子围绕Kerr黑洞的碰撞

Collision of two general geodesic particles around a Kerr black hole

Tomohiro Harada, Masashi Kimura

备注：
21 pages, 3 figures, minor correction
发表信息：
Phys.Rev.D83:084041,2011
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摘要：

我们得到了Kerr黑洞周围任意时空点处两个一般测地质量粒子和无质量粒子碰撞的质心能量的显式表达式。应用这一点，我们证明了CM能量只能在视界的极限内是任意高的，然后导出了两个一般测地粒子在视界附近碰撞的CM能量的公式，它是关于每个粒子的守恒量和极角的.我们提出的必要和充分条件的CM能量是任意高的每个粒子的守恒量。要获得任意高的CM能量，两个粒子中任何一个的角动量必须微调到临界值$L_{i}=Ω_{H}^{-1}E_{i}$，其中$Ω_{H}$是视界的角速度，$E_{i}$和$L_{i}$分别是粒子$i$（$=1,2$）的能量和角动量。我们表明，在直接碰撞的情况下，具有任意高的CM能量的碰撞可以发生在最大旋转的黑洞的视界附近，不仅在赤道，而且在以赤道为中心的带上。该带位于$\pm acos(\sqrt{3}-1)\simeq \pm 42.94^{\circ}$纬度之间。在最后一个稳定轨道粒子发生碰撞的情况下也是如此。

英文摘要：

We obtain an explicit expression for the center-of-mass (CM) energy of two colliding general geodesic massive and massless particles at any spacetime point around a Kerr black hole. Applying this, we show that the CM energy can be arbitrarily high only in the limit to the horizon and then derive a formula for the CM energy of two general geodesic particles colliding near the horizon in terms of the conserved quantities of each particle and the polar angle. We present the necessary and sufficient condition for the CM energy to be arbitrarily high in terms of the conserved quantities of each particle. To have an arbitrarily high CM energy, the angular momentum of either of the two particles must be fine-tuned to the critical value $L_{i}=Ω_{H}^{-1}E_{i}$, where $Ω_{H}$ is the angular velocity of the horizon and $E_{i}$ and $L_{i}$ are the energy and angular momentum of particle $i$ ($=1,2$), respectively. We show that, in the direct collision scenario, the collision with an arbitrarily high CM energy can occur near the horizon of maximally rotating black holes not only at the equator but also on a belt centered at the equator. This belt lies between latitudes $\pm acos(\sqrt{3}-1)\simeq \pm 42.94^{\circ}$. This is also true in the scenario through the collision of a last stable orbit particle.

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