Understanding accelerated frame in general relativity

[cramis1]

Hello,
apologies if this has been asked before but I couldn't find it upon searching...

My block to understanding general relativity has always been how the idea of gravity being the same as an accelerating frame leads to a a curved space-time?
What about the fact of not knowing whether you are in an accelerated frame or within a gravitational field results in the idea of a space-time and objects having the ability to bend space-time, and therefore, attract other objects?

Thanks
cram

 

[Dale]

Hi cramis1, welcome to PF!

What about the fact of not knowing whether you are in an accelerated frame or within a gravitational field results in the idea of a space-time and objects having the ability to bend space-time, and therefore, attract other objects?

I don't think that the equivalence principle leads directly to curved spacetime (at least I don't know the derivation if there is one). I think that it is more along the lines that the equivalence principle is a feature that we would like our theory of gravity to exhibit regardless of how the theory was obtained.

The equivalence principle is usually stated in terms of uniform acceleration or small regions of spacetime where tidal effects can be neglected. Curvature on the other hand deals with regions of spacetime where tidal effects cannot be neglected.

What is your knowledge of special relativity (SR)? Are you familiar with spacetime diagrams, four-vectors, and the geometric interpretation of SR?