Relativistic acceleration in noninertial frames of a line of objects

Abstract

A general solution to the problem of relativistic acceleration of point objects in the noninertial frame of any of the objects is given in one spatial dimension. The objects are initially at rest in a common inertial frame and accelerate until they are at rest in a second inertial frame. The starting time and position of each object, the acceleration rate of each object, and the number of objects are arbitrary. The solution gives the position and velocity of each object in the noninertial frame of the host object, and the proper time of each, as functions of the proper time of the host. The method is based on system states for a pair of objects, and it is found that there are nine series of states which cover all cases, including those in which objects are separated from the host by its Rindler horizon. The familiar problems of acceleration of an elastic rod and a (Born) rigid rod are treated, and a number of examples are given of spaceflight sequences for multiple craft in tandem.