Why is the average stiffness inside neutron stars approximately universal?

The accurate observations of neutron stars have deepened our knowledge of both general relativity and the properties of nuclear physics at large densities and low temperatures. Relating these observations to the microphysics that governs matter at these densities can sometimes be aided by approximate universal relations. One such relation connects the central pressure to the central energy density and the compactness of the star, and it has been found to be insensitive to the equation of state to a 10% level. In this talk, I will show that this relation can be interpreted as the average of the speed of sound squared in the interior of a star of a given compactness. Furthermore, I will show that for a class of equations of state, the universality is rooted in the behavior of the equation of state at energy densities below nuclear saturation, using post-Minkowskian expansions and geometric techniques.