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I am new to the forum and have a question on the logic of General Relativity. Correct me if I am wrong but my understanding is that according to Einstein's equivalence principle:

1) Freefall in gravity is the same as weightlessness in sufficiently small areas (so an accelerating frame can be seen as a inertial frame 'locally').

2) Gravitational acceleration is the same as any other accelerating reference frame.

3) But how do we then conclude that spacetime is curved by matter from the above logic.

Thanks

P.S I don't come from a physics background but I do have an interest in the area (you can call it my second passion) so it'd be helpful to keep the explanations simple :).