论文标题
标量自我力量理论中的助力法则
Flux-balance laws in scalar self-force theory
论文作者
论文摘要
辐射点粒子的运动可以用一系列的地球化学表示，其运动的“常数”随时间而缓慢地进化。这些运动常数的演变可以直接从运动的自力方程式确定。在时空对称性的情况下，情况简化了：不仅存在与这些对称性的运动共轭的常数，而且还存在可用的通量来确定其演变的保守电流。点粒子运动与保守电流的通量之间的这种关系是通量平衡定律。但是，存在与时空对称性无关的运动常数，这是Kerr时空中Carter常数的最显着示例。在本文中，我们首先使用符号电流和对称算子的技术提出了一种新的时空对称性的通量平衡定律，这也可以产生更通用的保守电流。然后，使用背景，地球运动是可以整合的事实，我们将在Kerr时空中为所有运动常数得出磁通平衡定律。为了简单起见，我们将本文的推导限制为标量自力更生问题。在将本文中的讨论概括为引力案例将是直接的，但在这种情况下，将这些结果转变为实用的磁通平衡法也将还有其他并发症。
The motion of a radiating point particle can be represented by a series of geodesics whose "constants" of motion evolve slowly with time. The evolution of these constants of motion can be determined directly from the self-force equations of motion. In the presence of spacetime symmetries, the situation simplifies: there exist not only constants of motion conjugate to these symmetries, but also conserved currents whose fluxes can be used to determine their evolution. Such a relationship between point-particle motion and fluxes of conserved currents is a flux-balance law. However, there exist constants of motion that are not related to spacetime symmetries, the most notable example of which is the Carter constant in the Kerr spacetime. In this paper, we first present a new approach to flux-balance laws for spacetime symmetries, using the techniques of symplectic currents and symmetry operators, which can also generate more general conserved currents. We then derive flux-balance laws for all constants of motion in the Kerr spacetime, using the fact that the background, geodesic motion is integrable. For simplicity, we restrict derivations in this paper to the scalar self-force problem. While generalizing the discussion in this paper to the gravitational case will be straightforward, there will be additional complications in turning these results into a practical flux-balance law in this case.
