Consider the x - t plane of an inertial observer in sr. a certain uniformly accelerated observer wishes to set up an orthonormal coordinate system. by exer. 21, 2.9, his world line is t(lambda) = a sinh lambda, x(lambda) = a cosh lambda, (5.96) where a is a constant and ax is his proper time (clock time on his wrist watch). show that the spacelike line described by eq. (5.96) with a as the variable parameter and a fixed is orthogonal to his world line where they intersect. changing a in eq. (5.96) then generates a family of such lines. show that eq. (5.96) defines a transformation from coordinates (t, x) to coordinates (a, a), which form an orthogonal coordinate system. draw these coordinates and show that they cover only one half of the original t x plane. show that the coordinates are bad on the lines so they really cover two disjoint quadrants, find the metric tensor and all the christoffel symbols in this coordinate system. this observer will do a perfectly good job, provided that he always uses christoffel symbols appropriately and sticks to events in his quadrant. in this sense, sr admits accelerated observers. the right-hand quadrant in these coordinates is sometimes called rindler space, and the boundary lines x=plusminus t bear some resemblance to the black-hole horizons we will study later.