论文标题
相对论双曲运动及其高阶运动量
Relativistic hyperbolic motion and its higher order kinematic quantities
论文作者
论文摘要
我们研究了观察者在1+1和1+3维的Minkowski SpaceTime中具有恒定适当加速的观察者运动的运动学。我们为所有运动量的所有运动量提供明确的公式，直到第四个适当的时间导数（SNAP）。在1+3的情况下，在最近的Pons和de Palol的工作之后[Gen. rel。坟墓。 51（2019）80]，获得加速度的矢量微分方程，该方程是通过考虑恒定适当加速度将其变成非线性二阶微分方程的，就半径向量的衍生物而言。此外，如果以双曲线函数的范围对速度进行了参数化，则获得一个微分方程来求解速度的参数f。与使用特定解决方案的PON和DE PALOL不同，在适当的时间s中线性，我们获得了一般解决方案，并使用它来为运动量数量计算更通用的表达式。作为副产品，我们获得了一类改良的Rindler双曲线世界，其特征是对运动量的组成部分的补充贡献。
We investigate the kinematics of the motion of an observer with constant proper acceleration (relativistic hyperbolic motion) in 1+1 and 1+3 dimensional Minkowski spacetimes. We provide explicit formulas for all the kinematic quantities up to the fourth proper time derivative (the Snap). In the 1+3 case, following a recent work of Pons and de Palol [Gen. Rel. Grav. 51 (2019) 80], a vectorial differential equation for the acceleration is obtained which by considering constant proper acceleration is turned into a nonlinear second order differential equation in terms of derivatives of the radius vector. If, furthermore, the velocity is parameterized in terms of hyperbolic functions, one obtains a differential equation to solve for the argument f(s) of the velocity. Differently from Pons and de Palol, who employed the particular solution, linear in the proper time s, we obtain the general solution and use it to work out more general expressions for the kinematical quantities. As a byproduct, we obtain a class of modified Rindler hyperbolic worldlines characterized by supplementary contributions to the components of the kinematical quantities.
