I need to use the N-P formalism to apply in my work so I'm trying first to apply in a simple case to understand better. So in this article ( https://arxiv.org/abs/1809.02764 ) which I'm using, they present a null tetrad for the Schwarszchild metric in pg.14 (with accordance with the...
So it worked out. The very strange thing that it leads, assuming only positive velocity, is that the velocity for a object leaves the ground at ##x'## is independent of the mass of the body!!! Do you follow that conclusion.
Yes! I really thought that the inequality was switched but didn't found my error. So you say I should think of $$f''(x')$$ as a negative number since it was the assumption and when I multiply both sides the inequality turns to a meaningful way? I will try it.
If f(x) is the function of the "ground": My first assumption is that in a certain $$\bar{x}$$, $$f''(\bar{x})=0$$, and from that point I will analyse the situation.
The object has initial energy $$E_0=\frac{mv^2}{2}+mgf(x),$$ then
$$v=\sqrt{\frac{2}{m}}\sqrt{E_0-mgf(x)}.$$
In each point the...