"Light cones tipping over" A common phrase used to show alleged time travel solutions in GR. Even a person like Kip Thorne uses it. But my question is, is that an accurate representation of GR in strong gravitational fields? The Schwarzschild metric expressed using the Eddington-Finkelstein coordinates show those "light cones tipping over", and eventually the radial and time coordinates reverse. But this reversal, and even the tipping over seems to me a peculiarity of the choice of coordinates. It seems to me that it is assumed that there is a particular relationship between the radial and time coordinate. That seems to be a rather liberal interpretation of the metric. Afteral nothing in the Minkowskian metric of ds2 = dt2 - dr2 implies that if dt2 becomes negative it must be considered space and if dr2 becomes negative it must be considered time. Any comments or explanations?