We contribute a publicly available set of tables and code to provide Equations of State (EoS) for matter at neutron star densities. Our EoSes are constrained only by input from hadron physics and fundamental principles, without feedback from neutron star observations, and so without relying on General Relativity. They can therefore be used to test General Relativity itself, as well as modified gravity theories, with neutron star observables, without logical circularity. We have adapted state of the art results from N N chiral potentials for the low-density limit, pQCD results for the asymptotically high-density EoS, and use monotonicity and causality as the only restrictions for intermediate densities, for the EoS sets to remain as modelindependent as is feasible today.

In this review we highlight a few physical properties of neutron stars and their theoretical treatment inasmuch as they can be useful for nuclear and particle physicists concerned with matter at finite density (and newly, temperature). Conversely, we lay out some of the hadron physics necessary to test General Relativity with binary mergers including at least one neutron star, in view of the event GW170817: neutron stars and their mergers reach the highest matter densities known, offering access to the matter side of Einstein's equations. In addition to minimum introductory material for those interested in starting research in the field of neutron stars, we dedicate quite some effort to a discussion of the Equation of State of hadron matter in view of gravitational wave developments; we address phase transitions and how the new data may help; we show why transport is expected to be dominated by turbulence instead of diffusion through most if not all of the star, in view of the transport coefficients that have been calculated from microscopic hadron physics; and we relate many of the interesting physics topics in neutron stars to the radius and tidal deformability.

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Neutron stars and their mergers provide the highest-density regime in which Einstein’s equations in full (with a matter source) can be tested against modified theories of gravity. But doing so requires a priori knowledge of the Equation of State from nuclear and hadron physics, where no contamination from computations of astrophysics observables within General Relativity has been built in. We extend the nEoS uncertainty bands, useful for this very purpose, to finite (but small) temperatures up to $$T=30$$ T = 30 MeV, given that the necessary computations in ChPT and in pQCD are already available in the literature. The T-dependent band boundaries will be provided through the COMPOSE repository and our own website.

We show how the specific latent heat is relevant to characterize the first-order phase transitions in neutron stars. Our current knowledge of this dynamical quantity strongly depends on the uncertainty bands of Chiral Perturbation Theory and of pQCD calculations and can be used to diagnose progress on the equation of state. We state what is known to be hadron-model independent and without feedback from neutron star observations and, therefore, they can be used to test General Relativity as well as theories beyond GR, such as modified gravity.