Can Special Relativity handle accelerations?
It is a common misconception that Special Relativity cannot handle accelerating objects or accelerating reference frames. It is claimed that general relativity is required because special relativity only applies to inertial frames. This is not true. Special relativity treats accelerating frames differently from inertial frames but can still deal with them. Accelerating objects can be dealt with without even calling upon accelerating frames. This error often comes up in the context of the twin paradox when people claim that it can only be resolved in general relativity because of acceleration. This is not the case. The only sense in which special relativity is an approximation when there are accelerating bodies is that gravitational effects such as generation of gravitational waves are being ignored. But of course there are larger gravitational effects being neglected even when massive bodies are not accelerating and they are small for many applications so this is not strictly relevant.
