Testing gravity with the latent heat of neutron star matter

The Seidov limit is a bound on the maximum latent heat that a presumed first-order phase transition of neutron-star matter can have before its excess energy density, not compensated by additional pressure, results in gravitational collapse. Because latent heat forces an apparent nonanalytic behaviour in plots correlating physical quantities (kinks in two-dimensional, ridges in three-dimensional ones), it can be constrained by data. As the onset of collapse depends on the intensity of gravity, testing for sudden derivative changes and, if they are large, breaching the Seidov limit would reward with two successive discoveries: such a phase transition (which could stem from hadron matter but also from a gravitational phase transition), and a modification of General Relativity (thus breaking the matter/gravity degeneracy). We illustrate the point with $f(R)=R+\alpha R^2$ metric gravity.