Black holes on eccentric orbits… what does it even mean? The hard (but fun) thing is that we work in General Relativity, where coordinates don’t have a physics inside. One can always change the coordinates as they want, so they can’t be used to define observables. The eccentricity of an orbit has to do, indeed, with the shape of the orbit itself, and that can be transformed away with suitable coordinates. So, does it even sense to measure the orbital eccentricity of black-hole binaries? The one thing we are allowed to do is to find a coordinate-free estimator in General Relativity that reduces to the eccentricity we all know and love in the Newtonian limit. This is possible! The right mathematical framework for this is something called “catastrophe theory”, a funny name, but Nick likes it.

Matteo Boschini, Nicholas Loutrel, Davide Gerosa, Giulia Fumagalli.
arXiv:2411.00098 [gr-qc].