Linear acceleration in flat space-time is a discipline that falls somewhere in-between Einsteinís special and general theories of relativity. The special theory is not quite applicable, because there is no single inertial frame of reference that covers accelerated movement.
Likewise, the general theory is not quite applicable. Acceleration as discussed here is not geodesic movement in a gravitational field. In a gravitational field, objects that are not disturbed in any other way move along geodesics in curved space-time.
However, acceleration is more closely related to special relativity than it is to general relativity, because it does not require curved spacetime due to gravity. It is also linked to the concept of inertia. Inertia is the resistance of all material object against being accelerated. Read more about inertia in this web article: =>
The Origin of Inertia.
Learn more about the fascinating subject of linear acceleration from a relativistic point of view by reading the attached pdf file (link below).
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