T = X which the upper red horizon lies along; these observers could however receive signals from events with T ≥ X if they stopped their acceleration and crossed this line themselves) nor could they have ever sent signals to events with T ≤ −X (events on or to the left of the line T = −X which the lower red horizon lies along; those events lie outside all future light cones of their past world line). Also, if we consider members of this set of accelerating observers closer and closer to the horizon, in the limit as the distance to the horizon approaches zero, the constant proper acceleration experienced by an observer at this distance (which would also be the G-force experienced by such an observer) would approach infinity. Both of these facts would also be true if we were considering a set of observers hovering outside the event horizon of a black hole, each observer hovering at a constant radius in Schwarzschild coordinates. In fact, in the close neighborhood of a black hole, the geometry close to the event horizon can be described in Rindler coordinates. Hawking radiation in the case of an accelerating frame is referred to as Unruh radiation. The connection is the equivalence of acceleration with gravitation. Geodesics The geodesic equations in the Rindler chart are easily obtained from the geodesic Lagrangian; they are Of course, in the original Cartesian chart, the geodesics appear as straight lines, so we could easily obtain them in the Rindler chart using our coordinate transformation. However, it is instructive to obtain and study them independently of the original chart, and we shall do so in this section. From the first, third, and fourth we immediately obtain the first integrals But from the line element we have where for timelike, null, and spacelike geodesics, respectively. This gives the fourth first integral, namely . This suffices to give the complete solution of the geodesic equations. In the case of null geodesics, from with nonzero , we see that the x coordinate ranges over the interval . The complete seven parameter family giving any null geodesic through any event in the Rindler wedge, is Plotting the tracks of some representative null geodesics through a given event (that is, projecting to the hyperslice ), we obtain a picture which looks suspiciously like the family of all semicircles through a point and orthogonal to