What are the minimum assumptions of general relativity?

For Special Relativity, it's that space-time is rotationally symmetric, translationally symmetric and locally isometric. According to Relativity Without Light, by N. David Mermin, from that you can prove that there is some maximum speed at which massless particles go and time dilation/length contraction, E=mc^2, etc.





I believe that you need the assumptions of special relativity together with Mach's equivalence principal, but I'm not really sure. Does anybody know?|||Those are not sufficient postulates to derive special relativity. Assumptions of homogeneity, isotropy, memorylessness, reciprocity, and relativity only imply the relationship between inertial frames up to a constant, but cannot determine if that constant is positive, negative or zero. Hence it is more usual to use the twin assumptions of the principle of relativity and the invariance of the spacetime interval. These two can be used to derive the tranformation laws of SR.





GR needs in addition the principle of equivlance. The Mach Principle - which is poorly defined in any event - is again not of itself sufficient. While Mach's Principle led Einstein in his thinking, the principle of equivlance is stonger and more robustly defined, and gives precise form to GR.|||Sure, gravity is equivalent to acceleration (principle of equivalence), but this does not quantify the source of gravity (the stress-energy tensor).

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|||General relativity is the result of Einstein's Field Equation. The Field Equation indicates that the curvature of space Tensor is directly proportional to the stress energy Tensor.


The ratio of curvature tensor to the stress energy Tensor is a constant equal to "G"

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|||General relativity is the result of Einstein's Field Equation. The Field Equation indicates that the curvature of space Tensor is directly proportional to the stress energy Tensor.


The ratio of curvature tensor to the stress energy Tensor is a constant equal to "G"

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|||Thus Einstein proved the validity of Newton's Universal constant "G".

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|||In addition to isotropy and space and time invariance, as you state, special relativity assumes that the speed of light is reference frame invariant. Mach's Principle is not a assumption, but something consistent and more precise can be derived from GR.





The two main assumptions one adds to get GR are the local principle of equivalence between gravity and acceleration (what curvature does) and that space-time curves in proportion to the mass energy tensor as defined by the Einstein Field Equations (the source of curvature).





I'm not sure what the latter means in terms of a qualitative principle analogous to the other principles. It gets a bit hand wavy in that regard, from what I've read. But basically, it goes something like the EFE's being the simplest and most "elegant" tensor representation that reduces to Newtonian physics in the proper limit.|||minimum assumptions:


1) everything in the universe is constantly in motion


2) in the absence of what is not, what is isn't.


3) matter is always attracted to itself