Speaker
Description
Understanding the extreme conditions inside neutron stars represents a
major challenge for Astrophysics. Here I present our investigation on
the behaviour of curvature invariants for a large ensemble
of neutron stars built with equations of state (EOSs) that satisfy
constraints from nuclear theory and perturbative QCD, as well as
measurements of neutron-star masses, radii, and gravitational waves from
binary neutron-star mergers. Surprisingly, our analysis reveals that
stars with negative Ricci scalar $\mathcal{R}$ are rather common, and
about $\sim 49\%$ of our EOSs produce one or more stars with Ricci
curvature that is negative somewhere inside the star. Furthermore, this
negative curvature is found mostly but not exclusively at the highest
densities and pressures, and predominantly for stiff EOSs. Furthermore,
using a well-known relation between the Ricci scalar and the trace
anomaly, $\Delta$, our analysis also allows us to determine the general
conditions under which the conformal symmetry of matter is broken and
restored in neutron stars. Finally, we determine a number of correlations
among the different scalar invariants and map the ranges of their allowed
values inside neutron stars.