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(Short abstract). In Galilean physics, the universality of free fall impliesan inertial frame, which in turns implies that the mass m of the falling bodyis omitted. Otherwise, an additional acceleration proportional to m/M wouldrise either for an observer at the centre of mass of the system, or for anobserver at a fixed distance from the centre of mass of M. These elementary,but overlooked, considerations fully respect the equivalence principle and theidentity of an inertial or a gravitational pull for an observer in the Einsteincabin. They value as fore-runners of the self-force and gauge dependency ingeneral relativity. The approximate nature of Galilei's law of free fall isexplored herein. When stepping into general relativity, we report how thegeodesic free fall into a black hole was the subject of an intense debate againcentred on coordinate choice. Later, we describe how the infalling mass and theemitted gravitational radiation affect the free fall motion of a body. Thegeneral relativistic self-force might be dealt with to perfectly fit into ageodesic conception of motion. Then, embracing quantum mechanics, real blackholes are not classical static objects any longer. Free fall has to handle theHawking radiation, and leads us to new perspectives on the varying mass of theevaporating black hole and on the varying energy of the falling mass. Along thepaper, we also estimate our findings for ordinary masses being dropped from aGalilean or Einsteinian Pisa-like tower with respect to the current state ofthe art drawn from precise measurements in ground and space laboratories, andto the constraints posed by quantum measurements. The appendix describes howeducation physics and high impact factor journals discuss the free fall.Finally, case studies conducted on undergraduate students and teachers arereviewed.

international journal of geometric methods in modern physics

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