A New Kind of Uniformly Accelerated Reference Frames

In the literature, a uniformly accelerated reference frame is defined as a set of observers who remain at rest with respect to a given observer Alice who is accelerating at a constant rate with respect to the instantaneously comoving inertial frames. Two observers Alice and Bob are said to be at rest with respect to each other if the time elapses on the clock of Alice during the passage of a light signal from Alice to Bob and back again always has the same value. By definition, two observers who at each instant are moving with the same velocity v(t) with respect to an inertial frame will remain at rest only when v(t) is a constant. Therefore, a set of observers who has a single acceleration is not said to constitute a uniformly accelerated reference frame. Instead, a uniformly accelerated reference frame is usually described by Rindler coordinate system ds = ξ̃dη̃ − dξ̃ − dy − dz, (2)