Title: Anomalous causality and the relativity of the event
Abstract: In gravity it proves convenient to identify the events by anchoring them to a set of free falling observers. This prescription has the advantage of naturally conveying the point of view of these observers.
In the presence of important fluctuations of the metric field one can calculate average distances between the events in this frame, but these, I will show, are not geodesic distances of any metric and portray an interesting ``average causal structure” that has no classical analogue.
At the same time, coordinate transformations between frames become probabilistic in the presence of these metric fluctuations. As an example I will consider the 1+1 dimensional model of JT gravity and discuss different localization in that framework. I will show that the location of the black hole horizon becomes blurred in most frames, in particular in the frame of free falling observers.