Curvature of spacetime is important interpretation of equotations of General relativity, but what I know this is just an interpretation without any experimental confirmation.
Many people, even many educated people believe, that curved spacetime of GR is confirmed by observed bending of light around Sun and also by bending of light in gravitational lensing observed in astronomy, but what I know, this is not true.
Bending of light is caused by gravity, because photons have effective mass (not invariant mass), it is also predicted by Newton gravity theory. GR just gives more precise level of bending which is in line with observed bending and accounts for relativity effects like time dilation. In other words bending of light is not confirmation of curvature of spacetime.
So I couldnt find any reasonable confirmation for curvature of spacetime apart from obvious confirmations of Lorentz factor change in line with predictions of SR and GR. But maybe somebody here will know better.
As you have rightly stated that bending of light can be explained by Newtonian Gravity also, accuracy apart. You have also rightly stated that there are no direct evidence for curvature of spacetime. I, and I am not alone, do not understand what is this curvature of spacetime in reality......those who are supporting this, also do not understand what is this curvature of spacetime in reality. You will be further confused that the path traced by lights and objects in curved spacetime is called as straightline, so if it is straightline by simple generation old definition of straightline, there should not be any curvature, but they say it is there ? Moreover light is also following curvature of spacetime and planets etc are also following curvature of spacetime around massive star ? So what exactly is the curvature of spacetime ? Is it curvature of space ? No it is not, but such mix up is present in literature too. If it is the curvature of space, then why it is initial speed dependent of the moving object ? Moreover you can create curvature of the space, only if it has materialistic influenciable property, but we are silent which aspect of space is responsible for this curvature.
Then we do not know how this curvatue can change if two objects are nearby, say two almost equal mass Neutron star are orbiting each other (Binary combination), then we do not know how do you get resultant curvature, consider the two binary BHs and it defies all logic. It is more than 100 years and we do not know how to solve these EFEs, still eluding.
Yes, I would agree that spacetime is a mathematical model, it is geometrical representation of gravity, and involves curvature etc, associating it with space or with anything realistic is bad...neither side should push it.
Please note spacetime is not space....
It is like when you solve a difficul stokes non linear equation in fluid dynamics and map it then the curve may involve many curvatures, these curvatures can be assigned certain physical meaning but strictly under mathematical interpretation. Associating such interpretation with Physical interim reality is bound to create problems.
