- Einstein's field equations are explicitly based on (interstellaire) spaces where normally gravity prevails, but which themselves are completely empty. There is no form of energy present (De Vlieger §14 en §16).
- All laws of physics have to be expressed in the field equations in such a way, that they are valid in all relevant coordinate systems having a single time coordinate. All laws of physics must therefore be covariant, as it is called in physical lingo.
The fourth chapter serves to generalize the other disciplines of physics, such as those of liquids and electrodynamics, for his theory of gravity. Finally, in the fifth chapter, the perihelion precession of Mercury and the deflection of light near heavy celestial bodies are discussed, in order to prove the correctness of his theory. Einstein also emphasizes in this chapter, that Newtons theory of gravity is consistent with his theory, and is still accurate enough for general use in everyday situations.
In the third chapter of his theory, therefore, I am mainly concerned with the two above-mentioned items.
Because these "empty" spaces are interstellar, they are principal based on an underlying spacetime that is more or less curved. I will call this spacetime 'timelike gravity spacetime (2 + 2)' to distinguish it from the spacelike Minkowski spacetime (3 + 1).
In Einstein's field equations, gravitational spacetime is not curved and is called the metric field. The field equations subsequently describe in what way the presence of, for example, a planet (matter / energy) curves this metric field. (The following section describes how this process is carried out in the field equations.) By starting with (interstellar) spaces, Einstein and his equations initially ended up with movements like those of the moons, the planets and the Sun.