Below is a copy of my poster “Time slicings of black holes”. It contrasts two different perspectives on Schwarzschild spacetime: by falling and static observers. More technically, I give a family of spacelike foliations which are orthogonal to the worldlines of observers freely-falling radially, and examine the resulting 3-spaces and simultaneity. These properties are contrasted with the static slicing described by the Schwarzschild coordinate t=const. My work is a reaction against the over-emphasis on the static slicing, which has led to many persistent misconceptions, whereas I emphasise space and time are relative. (Of course the 4-dimensional spacetime is independent of the slicing.)
The original version was presented at the general relativity conference GR21 in New York City, 2016, and subsequently other conferences. Below is the 2017 updated version, first presented at the quantum gravity conference “Probing the spacetime fabric” in Trieste, Italy, 2017. [Brief brag moment: luminaries who have viewed and discussed it with me include Jiří Podolský at GR21, and Piotr Chruściel at the “Between Geometry and Relativity” program in Vienna, Austria, 2017.]
A PNG image version is shown below, you can also access a PDF version or even the original.