RT Journal Article T1 Ridges in rotating neutron-star properties due to first order phase transitions A1 Navarro Moreno, Pablo A1 Llanes Estrada, Felipe José A1 Lope Oter, Eva AB We identify combinations of observables for rotating neutron stars that can one day bear on the question of whether there can be first order phase transitions in the neutron matter therein. We employ the Hartle–Thorne theory for stationary, rotating neutron stars at conventional angular velocities (in the conventional pulsar and millisecond pulsar ranges) and extract threedimensional sections of the ellipticity or the dynamical angular momentum as function of the star’s mass and angular velocity. An eventual first order phase transition in the equation of state (EoS) leaves a clear ridge (nonanalyticity) in these observables, akin to the sudden kink in popular mass–radius diagrams for static stars. Finally, we observe that static neutron stars in General Relativity (GR) will fail to be compact enough for the light ring’s position at 𝑟 = 3𝑀 to be outside the star, except for the most extreme equations of state. The outer light ring of a rotating star might however be formed unless the EoS softens too much, and its eventual detection can then be used to constrain the EoS (or the gravity theory). PB Elsevier SN 0003-4916 YR 2023 FD 2023 LK https://hdl.handle.net/20.500.14352/88862 UL https://hdl.handle.net/20.500.14352/88862 LA eng NO P. N. Moreno, F. J. Llanes-Estrada, and E. Lope-Oter, Annals of Physics 459, 169487 (2023). NO European Commission NO Ministerio de Ciencia, Innovación y Universidades (España) NO Universidad Complutense de Madrid DS Docta Complutense RD 9 abr 2025