It is the GRADIENT of the gravitational field that causes objects to curve in space; ie accelerate. Space whose gravitational field (components of its metric) is a constant cause all the effects of gravity except for acceleration.
For instance, a Minkowski metric describes an Inertial System, where only the so-called "mass" of an object is felt.
Proving the Relativistic Energy-Momentum relation, the hard way and the easier way.
This adds the proof for the relativistic mass effects from motion, proving that gravity causes it.
Two reference frames in motions are not symmetrical. A system at rest on the surface of a planet moves faster in time than a moving system. This is not the case using just Special Relativity. This is proven just using the gravitational metric field in General Relativity.
