Einstein (1908) tried - as a preliminary in the framework of special relativity - also to include accelerated frames within the relativity principle. In the course of this attempt he recognized that for any single moment of acceleration of a body

**one can define an inertial reference frame in which the accelerated body is temporarily at rest.**
It follows that in accelerated frames defined in this way, the application of the constancy of the speed of light to define simultaneity is restricted to small localities. However, the

equivalence principle that was used by Einstein in the course of that investigation, which expresses the equality of inertial and gravitational mass and the equivalence of accelerated frames and homogeneous gravitational fields, transcended the limits of special relativity and resulted in the formulation of general relativity.

^{
}Nearly simultaneously with Einstein, also Minkowski (1908) considered the special case of uniform accelerations within the framework of his space-time formalism. He recognized that the world-line of such an accelerated body corresponds to a

hyperbola. This notion was further developed by Born (1909) and Sommerfeld (1910), with Born introducing the expression "

hyperbolic motion". He noted that

**uniform acceleration can be used as an approximation for any form of acceleration within special relativity**.

In addition,

Harry Bateman and

Ebenezer Cunningham (1910) showed that Maxwell's equations are invariant under a much wider group of transformation than the Lorentz-group, i.e., the so-called "

conformal transformations". Under those transformations

**the equations preserve their form for some types of accelerated motions**. A general covariant formulation of electrodynamics in Minkowski space was eventually given by

Friedrich Kottler (1912), whereby his formulation is also valid for general relativity.

Concerning t

**he further development of the description of accelerated motion in special relativity**, the works by Langevin and others for rotating frames (

Born coordinates), and by

Wolfgang Rindler and others for uniform accelerated frames (

Rindler coordinates) must be mentioned.