Initially I thought in special relativity the velocity was constant, whereas general relativity allowed treatment of accelerated frames as well.
But now I have heard that SR is only valid locally?
Answer
What is “special” and what is “general” in Relativity?
The "special" in special relativity refers to the fact that it is not a universal theory. Predictions made by special relativity only apply under certain special circumstances. Those special circumstances are where gravitation is not present or can essentially be ignored.
Initially I thought in special relativity the velocity was constant, whereas general relativity allowed treatment of accelerated frames as well.
You'll see a number of places that claim that special relativity only works in (Newtonian) inertial frames. This is not the case, any more than is the claim that Newtonian mechanics only works in (Newtonian) inertial frames. One way to think of special relativity is that it corrects Newton's three laws of motion (but not Newton's law of gravitation) for the fact that the speed of light is finite.
But now I have heard that SR is only valid locally?
Gravitation is undetectable at a sufficiently small scale. Since special relativity rather than Newtonian mechanics provides the "correct" physics when gravitation is not present, one of the key precepts of general relativity is that general relativity must be compatible with special relativity locally. This precept is built-in into general relativity.
"Locally" means has a different meaning to mathematicians and physicists. Physicists care about what can be measured. If you can't measure it, it doesn't exist (at least not until better instruments become available). This means "locally" depends on how much mass-energy is nearby and on how good ones instrumentation is. "Locally" in the vicinity of a black hole is a rather small region of space-time. "Locally" is a rather large region in the middle of a billion light year diameter void in space.
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