Acceleration in special relativity
This chapter considers the applications of special relativity to accelerated motion. Accelerated worldlines have some unusual properties in relation to the event horizon. A spacetime coordinate system can be developed using the worldlines of accelerated particles, just as the worldlines of free particles comprise a coordinate system for Minkowski space. The chapter shows worldlines associated with different values of the acceleration. The region to the right of the event horizon can thus be covered by two coordinate grids: the Cartesian grid of an inertial observer and the hyperbolic grid of accelerated observers. Motion in a noninertial frame can be treated using the mechanics. The rest space of an observer is defined as the local three-dimensional space orthogonal to the timelike basis vector. A tetrad is a local set of orthonormal vectors, where one is timelike and three are spacelike.