[论文解读] Acceleration of colliding shells around a black hole -- Validity of test particle approximation in BSW process

Masashi Kimura, Ken-ichi Nakao+1 more|arXiv (Cornell University)|Oct 26, 2010

Astrophysical Phenomena and Observations被引用 3

一句话总结

本文通过建模极端黑洞周围的碰撞尘埃壳，研究了在BSW过程中测试粒子近似方法的有效性，表明其自引力效应在无穷远处可观测的质心能量上施加了上限，暗示由于粒子自身引力导致的物理能量上限存在于BSW机制中。

ABSTRACT

Recently, Banados, Silk and West (BSW) showed that the total energy of two colliding test particles has no upper limit in their center of mass frame in the neighborhood of an extreme Kerr black hole, even if these particles were at rest at infinity in the infinite past. We call this mechanism the BSW mechanism or BSW process. The large energy of such particles would generate strong gravity, although this has not been taken into account in the BSW analysis. A similar mechanism is seen in the collision of two spherical test shells in the neighborhood of an extreme Reissner-Nordstrom black hole. In this paper, in order to draw some implications concerning the effects of gravity generated by colliding particles in the BSW process, we study a collision of two spherical dust shells, since their gravity can be exactly treated. We show that the energy of two colliding shells in the center of mass frame observable from infinity has an upper limit due to their own gravity. Our result suggests that an upper limit also exists for the total energy of colliding particles in the center of mass frame in the observable domain in the BSW process due the gravity of the particles.

研究动机与目标

• 评估在极端Kerr黑洞附近，BSW过程中预测质心能量无限的测试粒子近似方法的有效性。
• 研究碰撞粒子产生的引力是否对总碰撞能量施加物理上限。
• 通过精确处理其自引力，建立两个球形尘埃壳的碰撞模型，作为对测试粒子模型的更真实替代。
• 确定尽管BSW机制预测能量无界，但可观测的碰撞壳质心能量是否仍保持有限。

提出的方法

• 建模两个球形尘埃壳向极端Reissner-Nordström黑洞坍缩，使用爱因斯坦方程的尘埃壳精确解。
• 在壳面应用连接条件，推导壳的动力学及其碰撞行为。
• 在碰撞壳的局部静止参考系中计算质心能量，然后将其转换为无穷远处观测到的能量。
• 分析当壳接近视界时质心能量的行为，重点关注其自引力的作用。
• 将结果与测试粒子模型下的BSW预测进行比较，以评估粒子自身引力的影响。

实验结果

研究问题

• RQ1 在BSW过程中，碰撞粒子的自引力是否对无穷远处可观测的质心能量施加有限上限？
• RQ2 当考虑其自身引力时，极端黑洞附近碰撞尘埃壳在质心参考系中的能量行为如何？
• RQ3 由于忽略了粒子自身引力场，测试粒子近似在BSW过程中在多大程度上失效？
• RQ4 当考虑碰撞壳自身引力效应时，可观测域中的碰撞能量是否仍可能无界？

主要发现

• 由于其自引力，从无穷远处测量的两个碰撞尘埃壳的质心能量受到上界限制。
• 可观测质心能量的上限源于壳自身引力场对其动力学和碰撞的反作用。
• 该结果表明，BSW机制预测的无限能量在完全自洽的引力模型中被否定。
• 能量的有限上界是壳质量及其所产生曲率的直接结果，这种曲率阻止了无限能量的累积。