从伽利略到爱因斯坦自由降落的规范依赖性和自作用力，致密恒星落入黑洞，霍金辐射和比萨斜塔在广义相对论百年纪念
Gauge dependence and self-force from Galilean to Einsteinian free fall, compact stars falling into black holes, Hawking radiation and the Pisa tower at the general relativity centennial
摘要：
（简短摘要）。在伽利略物理学中，自由降落的普适性意味着惯性系，这反过来意味着下落物体的质量m被忽略。否则，一个与m/M成比例的附加加速度将对位于系统质心的观测者或对位于距离M质心固定距离的观测者产生。这些基本的，但被忽视的考虑充分尊重等效原理和惯性或引力的爱因斯坦舱中的观察者的身份。他们被认为是广义相对论中自作用力和规范依赖性的先驱。本文探讨了伽利略自由降落定律的近似性质。当步入广义相对论，我们报告如何测地线自由降落到一个黑洞是一个激烈的辩论的主题再次集中在坐标的选择。随后，我们描述了下落的质量和发射的引力辐射如何影响物体的自由降落运动。广义相对论性的自作用力可以被处理成完全符合运动的测地线概念。然后，接受量子力学，真正的黑洞不再是经典的静态物体。自由降落必须处理霍金辐射，并引导我们对蒸发的黑洞的变化质量和下落质量的变化能量有新的看法。沿着这篇论文，我们还估计了我们的发现，从伽利略或爱因斯坦比萨塔相对于目前的技术水平从地面和空间实验室的精确测量，并由量子测量所构成的约束。附录描述了教育物理学和高影响因子期刊如何讨论自由降落。最后，对本科生和教师进行的案例研究进行了回顾。
英文摘要：
(Short abstract). In Galilean physics, the universality of free fall implies an inertial frame, which in turns implies that the mass m of the falling body is omitted. Otherwise, an additional acceleration proportional to m/M would rise either for an observer at the centre of mass of the system, or for an observer at a fixed distance from the centre of mass of M. These elementary, but overlooked, considerations fully respect the equivalence principle and the identity of an inertial or a gravitational pull for an observer in the Einstein cabin. They value as fore-runners of the self-force and gauge dependency in general relativity. The approximate nature of Galilei's law of free fall is explored herein. When stepping into general relativity, we report how the geodesic free fall into a black hole was the subject of an intense debate again centred on coordinate choice. Later, we describe how the infalling mass and the emitted gravitational radiation affect the free fall motion of a body. The general relativistic self-force might be dealt with to perfectly fit into a geodesic conception of motion. Then, embracing quantum mechanics, real black holes are not classical static objects any longer. Free fall has to handle the Hawking radiation, and leads us to new perspectives on the varying mass of the evaporating black hole and on the varying energy of the falling mass. Along the paper, we also estimate our findings for ordinary masses being dropped from a Galilean or Einsteinian Pisa-like tower with respect to the current state of the art drawn from precise measurements in ground and space laboratories, and to the constraints posed by quantum measurements. The appendix describes how education physics and high impact factor journals discuss the free fall. Finally, case studies conducted on undergraduate students and teachers are reviewed.
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