This is probably something I should know already, but... (sigh). OK, so we can't just look at a metric (e.g., black hole in Schwarzschild coords) and deduce something physically weird at ##r = 2M##, because that's just an artifact of the coordinate system -- the curvature tensor remains finite on that surface, and there are other coord systems in which the metric looks nicer. Also, there are spacetimes (e.g., Rindler) which have horizons even though they're globally flat. We have the weirdness that an ingoing radial geodesic can cross a black hole horizon and continue down to the singularity, but an initially-outgoing radial geodesic (started from inside the horizon) can't get out, and quickly turns around to fall inward again. Is there a way to easily recognize such behaviour (i.e., a 1-way horizon) using coordinate-independent techniques, without having to solve and analyze the full equations of motion? E.g., some tensor condition involving Killing vectors? Degeneracy of 1 or more degrees of freedom? Other?