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GR: Fachverband Gravitation, Relativistische Astrophysik und Kosmologie
GR 5: Relativistic Astrophysics I
GR 5.2: Talk
Tuesday, March 17, 2026, 16:30–16:45, KH 01.016
Curvature invariants and trace anomaly in neutron stars — •Iván Garibay1,2, Christian Ecker1, and Luciano Rezzolla1,3,4 — 1Institut für Theoretische Physik, Goethe Universität, Max-von-Laue-Str. 1, 60438 Frankfurt am Main, Germany — 2Instituto de Astronomía, Universidad Nacional Autónoma de México, Ciudad de México, CDMX 04510, Mexico — 3School of Mathematics, Trinity College, Dublin 2, Ireland — 4Frankfurt Institute for Advanced Studies, Ruth-Moufang-Str. 1, 60438 Frankfurt am Main, Germany
We investigate 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 R are rather common, and about ∼ 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, Δ, 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.
Keywords: neutron stars; equation of state; trace anomaly; curvature scalars