# General Relativity an inevitable consequence of the constancy of light-speed and the equivalence principle: Is this really true?

Quite a long time ago, longer than I'd like to admit, I had heard what is said in the title -- that General relativity is the inevitable result of the constancy of the speed of light and the equivalence principle.

This excited me greatly, and perhaps a bit arrogantly, convinced me that I could derive much of it myself, after all I only had but two things to consider.

I did manage to complete that task for the most part in special relativity, but the general theory has me stumped.

Let me explain what I do currently think is possible to ascertain based on these postulates.

The effect of gravitational time dilation comes directly from the equivalence principle, and using the concept of local inertial frames can produce a set of kinematics that predict how falling objects appear to move through fields of gravitational acceleration.

Thusly, from all I currently know, given a defined "acceleration to stay stationary" at every point in space, I can predict how a falling object moves, HOWEVER, what I cannot yet predict is what that "acceleration to stay stationary at every point" is.

Naively I might assume it's simply the Newtonian expression $$a=\frac{GM}{r^{2}}$$, but unfortunately I have found that it is not.

I've been racking my brain for quite some time and can not yet see how these postulates in combination imply a specific field configuration.

It seems to me that any if not many smooth acceleration distributions over space satisfy the equivalence principle, conserve energy, and locally satisfy special relativity, and so again I see no reason for a specific one to arise.

With that, I have surmised roughly two options to explain my futility, It is my own ignorance that is the problem, or there is some bit of information that I'm lacking.

So I ask once again, do these two postulates result in the ENTIRETY of general relativity, or is there some other assumption that I need to make to arrive at it?

I will be eternally grateful for anyone that can help me out of this rut, truly.

• Did you look at other questions relating to this topic on this site? The question sounds very much like a duplicate. Commented Jul 31 at 3:58
• @FlatterMann I have looked, I’ve been looking all day. Perhaps I’ve missed something, and if I did I would be very thankful if you linked it, but nothing I’ve found directly addresses my concerns: What information/postulate am I missing, is there a set of postulates that inevitably lead to GR. Commented Jul 31 at 3:59

• OK, good. Then "all" that the equivalence principle tells you is that objects move on geodesics in curved spacetime (which is quite a lot already). The difference between the various theories of gravity is in how the spacetime gets curved. IIRC GR is the simplest theory that uses the whole stress-energy-momentum tensor $T$. Some earlier attempts (like Nordstrom's) used only the trace of $T$, or some particular elements like $T_{00}$ (the energy flux). Commented Aug 1 at 19:43