论文标题
相对论力学的协变
A covariant formulation of relativistic mechanics
论文作者
论文摘要
围绕紧凑型物体和其他环境因素的积聚磁盘偏离了大地运动。不幸的是，建立这种相对论轨迹的运动方程并不像牛顿力学中那么简单。一般（或Lorentz）协方差的原理和质量壳约束使得很难参数物理上足够的4 forces。在这里，我们建议解决这个旧问题的解决方案。我们将框架应用于几种保守和耗散力量。特别是，我们提出了对胡克定律和恒力的协方差制剂，并计算由于灰尘，气体和辐射介质中的重力和硬球碰撞而引起的阻力。我们恢复并协变扩展了已知的力量，例如爱泼斯坦·德拉斯（Epstein Drag），钱德拉斯卡（Chandrasekhar）的动力摩擦和poynting-robertson拖动。还考虑了可变质量效应，即Hoyle-Lyttleton积聚和可变质量火箭。我们以两种应用结束：1。自由落体春天。我们发现，胡克定律通过有效的反de保姆潮汐力纠正了偏差方程。 2。黑洞的拖曳。我们从数字上计算了支持类似粉尘的吸积盘的Schwarzschild背景上的一些轨迹。
Accretion disks surrounding compact objects, and other environmental factors, deviate satellites from geodetic motion. Unfortunately, setting up the equations of motion for such relativistic trajectories is not as simple as in Newtonian mechanics. The principle of general (or Lorentz) covariance and the mass-shell constraint make it difficult to parametrize physically adequate 4-forces. Here, we propose a solution to this old problem. We apply our framework to several conservative and dissipative forces. In particular, we propose covariant formulations for Hooke's law and the constant force, and compute the drag due to gravitational and hard-sphere collisions in dust, gas and radiation media. We recover and covariantly extend known forces such as Epstein drag, Chandrasekhar's dynamical friction and Poynting-Robertson drag. Variable-mass effects are also considered, namely Hoyle-Lyttleton accretion and the variable-mass rocket. We conclude with two applications: 1. The free-falling spring. We find that Hooke's law corrects the deviation equation by an effective Anti-de Sitter tidal force; 2. Black hole infall with drag. We numerically compute some trajectories on a Schwarzschild background supporting a dust-like accretion disk.
