Bogoslovsky-Finsler时空中的测地线运动
Geodesic motion in Bogoslovsky-Finsler Spacetimes
AI总结：
本研究探究Bogoslovsky-Finsler形变的平面引力波背景下有质量粒子的测地线运动，利用部分破缺Carroll对称性积分测地线方程，验证类时测地线横向坐标与原引力波一致，并将理论推广到齐次pp波及Finsler-Friedmann-Lemaitre模型。
摘要：
我们研究了爱因斯坦广义相对论中平面引力波的Finsler形变背景下有质量粒子的自由运动。该形变是Bogoslovsky提出的单参数相对论Finsler结构族的弯曲版本，这类结构在Cohen与Glashow的非常狭义相对论群ISIM(2)的特定形变下保持不变。我们利用Baldwin-Jeffery-Rosen坐标推导得到的部分破缺Carroll对称性，可对测地线方程进行积分。对于任意取值的Bogoslovsky-Finsler参数$b$，类时Finsler测地线的横向坐标都与底层平面引力波的横向坐标完全一致。随后我们将底层平面引力波替换为爱因斯坦-麦克斯韦方程的齐次pp波解。最后我们将该理论推广至Finsler-Friedmann-Lemaitre模型。
英文摘要：
We study the free motion of a massive particle moving in the background of a Finslerian deformation of a plane gravitational wave in Einstein's General Relativity. The deformation is a curved version of a one-parameter family of Relativistic Finsler structures introduced by Bogoslovsky, which are invariant under a certain deformation of Cohen and Glashow's Very Special Relativity group ISIM(2). The partially broken Carroll Symmetry we derive using Baldwin-Jeffery-Rosen coordinates allows us to integrate the geodesics equations. The transverse coordinates of timelike Finsler-geodesics are identical to those of the underlying plane gravitational wave for any value of the Bogoslovsky-Finsler parameter $b$. We then replace the underlying plane gravitational wave by a homogenous pp-wave solution of the Einstein-Maxwell equations. We conclude by extending the theory to the Finsler-Friedmann-Lemaitre model.
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