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arXiv 1010.0962gr-qcastro-ph.HEhep-th
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Kerr黑洞周围最内层稳定圆轨道粒子的碰撞

Collision of an innermost stable circular orbit particle around a Kerr black hole

Tomohiro Harada, Masashi Kimura

备注：
24 pages, 2 figures, accepted for publication in Physical Review D, minor correction
发表信息：
Phys.Rev.D83:024002,2011
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摘要：

导出了两个静止质量相同的粒子在Kerr黑洞赤道面上近视界碰撞的质心能量的一般公式。然后，我们将这个公式应用于一个从最内层稳定圆轨道（ISCO）坠落并与视界附近的另一个粒子碰撞的粒子。发现对于一个近最大旋转的黑洞，CM能量$E_{\rm cm}$的最大值由$E_{\rm cm}/(2m_{0})\simeq 1.40/\sqrt[4]{1-a_{*}^{2}}$给出，其中$m_{0}$是每个粒子的静止质量，$a_{*}$是无量纲Kerr参数.这与已知的粒子的上限相一致，该粒子在无穷远处开始静止，其系数为2。此外，我们还考虑了一个粒子与另一个粒子在ISCO上的碰撞，发现最大CM能量由$E_{\rm cm}/(2m_{0})\simeq 1.77/\sqrt[6]{1-a_{*}^{2}}$给出。鉴于ISCO的天体物理意义，这一结果意味着，如果我们可以采取黑洞自旋或$a_{*}\to 1$的最大极限，粒子可以碰撞周围的旋转黑洞具有任意高的CM能量，没有任何人为的微调在天体物理学的背景下。另一方面，即使我们考虑到索恩对自旋参数的限制，高度或中度相对论性碰撞预计会很自然地发生，因为$E_{\rm cm}/(2m_{0})$在视界附近需要6.95（最大）和3.86（一般），而在ISCO上$a_{*}=0.998$需要4.11（最大）和2.43（一般）。这意味着，在快速旋转的超大质量黑洞周围，紧凑物体的高速碰撞是自然预期的。吸积流到一个快速旋转的黑洞的影响也进行了讨论。

英文摘要：

We derive a general formula for the center-of-mass (CM) energy for the near-horizon collision of two particles of the same rest mass on the equatorial plane around a Kerr black hole. We then apply this formula to a particle which plunges from the innermost stable circular orbit (ISCO) and collides with another particle near the horizon. It is found that the maximum value of the CM energy $E_{\rm cm}$ is given by $E_{\rm cm}/(2m_{0})\simeq 1.40/\sqrt[4]{1-a_{*}^{2}}$ for a nearly maximally rotating black hole, where $m_{0}$ is the rest mass of each particle and $a_{*}$ is the nondimensional Kerr parameter. This coincides with the known upper bound for a particle which begins at rest at infinity within a factor of 2. Moreover, we also consider the collision of a particle orbiting the ISCO with another particle on the ISCO and find that the maximum CM energy is then given by $E_{\rm cm}/(2m_{0})\simeq 1.77/\sqrt[6]{1-a_{*}^{2}}$. In view of the astrophysical significance of the ISCO, this result implies that particles can collide around a rotating black hole with an arbitrarily high CM energy without any artificial fine-tuning in an astrophysical context if we can take the maximal limit of the black hole spin or $a_{*}\to 1$. On the other hand, even if we take Thorne's bound on the spin parameter into account, highly or moderately relativistic collisions are expected to occur quite naturally, for $E_{\rm cm}/(2m_{0})$ takes 6.95 (maximum) and 3.86 (generic) near the horizon and 4.11 (maximum) and 2.43 (generic) on the ISCO for $a_{*}=0.998$. This implies that high-velocity collisions of compact objects are naturally expected around a rapidly rotating supermassive black hole. Implications to accretion flows onto a rapidly rotating black hole are also discussed.

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