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arXiv 1005.1815gr-qchep-th
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受约束哈密顿系统的运动常数:带电旋转黑洞周围的粒子

Constants of Motion for Constrained Hamiltonian Systems: A Particle around a Charged Rotating Black Hole

Takahisa Igata, Tatsuhiko Koike, Hideki Ishihara

摘要:

我们讨论了弯曲时空中外场作用下粒子的运动常数,同时考虑到粒子轨道的重参数化不变性所引起的哈密顿约束。作为运动常数存在的充分必要条件,我们得到了一组具有层次结构的方程,它被理解为Killing张量方程的推广.它也是传统论点的推广,因为它包括守恒条件仅在相空间中的约束表面上成立的情况。在这种情况下,它示出的运动常数是与共形的Killing张量。我们应用层次方程,并找到在黑洞时空中的磁场的带电粒子的情况下的运动常数。我们还证明了引力场和电磁磁场的存在,其中带电粒子具有与共形Killing张量相关的运动常数。

英文摘要:

We discuss constants of motion of a particle under an external field in a curved spacetime, taking into account the Hamiltonian constraint which arises from reparametrization invariance of the particle orbit. As the necessary and sufficient condition for the existence of a constant of motion, we obtain a set of equations with a hierarchical structure, which is understood as a generalization of the Killing tensor equation. It is also a generalization of the conventional argument in that it includes the case when the conservation condition holds only on the constraint surface in the phase space. In that case, it is shown that the constant of motion is associated with a conformal Killing tensor. We apply the hierarchical equations and find constants of motion in the case of a charged particle in an electro-magnetic field in black hole spacetimes. We also demonstrate that gravitational and electro-magnetic fields exist in which a charged particle has a constant of motion associated with a conformal Killing tensor.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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