论文标题
使用高斯定理在Schwarzschild背景中偶极子磁场中带电信号的挠度
Deflection of charged signals in a dipole magnetic field in Schwarzschild background using Gauss-Bonnet theorem
论文作者
论文摘要
本文研究了弱场近似中施瓦茨柴尔兹柴尔德时空背景中偶极磁场中带电颗粒的挠度。为了计算挠度角，我们使用jacobi度量标准和高斯定理。由于相应的Jacobi公制是Randers类型的Finsler指标，因此我们同时使用示波器的Riemannian公制方法和广义的Jacobi公制方法。获得挠度角至第四阶，并讨论了磁场的效果。发现当磁性偶极子将其旋转角动量与磁场平行（或反平行）时，磁性偶极子将增加（或减小）带正电信号的偏转角。有人认为，不同旋转方向的挠度角度的差异可以看作是Finsler指标不可逆性的Finslerian效应。在这种情况下，偏转角的相似性与Kerr时空的相似性使我们能够在后一种情况下直接使用重力镜头。明显角度对磁场的依赖性表明，通过测量这些角度，磁偶极子可能会受到约束。
This paper studies the deflection of charged particles in a dipole magnetic field in Schwarzschild spacetime background in the weak field approximation. To calculate the deflection angle, we use Jacobi metric and Gauss-Bonnet theorem. Since the corresponding Jacobi metric is a Finsler metric of Randers type, we use both the osculating Riemannian metric method and generalized Jacobi metric method. The deflection angle up to fourth order is obtained and the effect of the magnetic field is discussed. It is found that the magnetic dipole will increase (or decrease) the deflection angle of a positively charged signal when its rotation angular momentum is parallel (or antiparallel) to the magnetic field. It is argued that the difference in the deflection angles of different rotation directions can be viewed as a Finslerian effect of the non-reversibility of the Finsler metric. The similarity of the deflection angle in this case with that for the Kerr spacetime allows us to directly use the gravitational lensing results in the latter case. The dependence of the apparent angles on the magnetic field suggests that by measuring these angles the magnetic dipole might be constrained.
