The General Theory of Relativity tells us gravity is not a force, gravitational fields don’t exist. Objects tend to move on straight paths through curved spacetime.
The basic principles of general relativity are:
● The geodesic postulate: free falling particles move along geodesics of space-time with the proper time
● The principle of equivalence: inertial mass
● By a proper choice of the coordinate system, it is possible to make the metric locally flat in each point
The Riemann tensor is defined as:
, are the Christoffel symbols.
For a second-order tensor holds:
The following holds:
The Ricci tensor is a contraction of the Riemann tensor:
which is symmetric:
The Bianchi identities are:
The Einstein tensor is given by:
With the variational principle
For empty space this is equivalent to
The Einstein equations are 10 independent equations, which are of second order in
The most general form of the field equations is:
Do you think that a freely falling object will radiate electromagnetic radiation or not? Are we simply all accelerating according to our interaction with matter (Earth in our case)? Until we can devise an experiment that can test this, we will only continue to guess and make assumptions.