I understood from lectures that the metric of a spacetime was absolute: It does not depend upon the test charge we put inside. Indeed, all the calculation our professor carried out were independent of the type of particle that "traveled" over that curved metric.
But then, when one tries to define the notion of particle in general curved backgrounds we notice that, since Poincaré invariance doesn't hold in general spacetimes, we cannot really define such a notion in an observer-independent way. So, the question is: Since we live in curved spacetime, how can one speak about "particles" at CERN-LHC?
Possible answer: for the particles themselves, metric is not curved. But then the metric does depends upon the kind of particle that you put inside, so the whole formulas are wrong, or incomplete, because they need a more term to indicate the particle mass, so.. are there some logical mistakes anywhere? In my reasoning or in physics?