利用拉格朗日量求解黑洞背景下自由光子的运动

Solving the motion of free photons in black hole background via Lagrangian

利用拉格朗日量求解力学问题是一种很有用的方法.本文将借助于拉格朗日量求解黑洞时空背景下自由光子的运动,在求得光子的四速度之后,借助于机械能守恒定律,考察具有不同能量的光子在黑洞背景下所允许的运动范围.随后根据力学中运动学反问题,最终得到光子的运动轨迹.

Solving mechanical problems with Lagrangian is a very useful method.In this paper,the motion of free photons in the background of a black hole is solved by means of Lagrangian.After obtaining the four velocities of photons,the allowable motion range of photons with different energies is studied by means of the law of conservation of mechanical energy.Then,according to the inverse problem of kinematics in mechanics,the trajectory of photons is finally obtained.