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Rigid (Uniform) rotation is usually assumed when investigating the properties of mature neutron stars (NSs). Although it simplifies their description, it is an assumption because we cannot observe the NS's innermost parts. Here, we analyze the structure of NSs in the simple case of ''almost rigidity,'' where the innermost and outermost parts rotate with different angular velocities. This is motivated by the possibility of NSs having superfluid interiors, phase transitions, and angular momentum transfer during accretion processes. We show that, in general relativity, the relative difference in angular velocity between different parts of an NS induces a change in the moment of inertia compared to that of rigid rotation. The relative change depends nonlinearly on where the angular velocity jump occurs inside the NS. For the same observed angular velocity in both configurations, if the jump location is close to the star's surface-which is possible in central compact objects (CCOs) and accreting stars-the relative change in the moment of inertia is close to that of the angular velocity (which is expected due to total angular momentum aspects). If the jump occurs deep within the NS, for instance, due to phase transitions or superfluidity, smaller relative changes in the moment of inertia are observed; we found that if it is at a radial distance smaller than approximately $40\%$ of the star's radius, the relative changes are negligible. Additionally, we outline the relevance of systematic uncertainties that nonrigidity could have on some NS observables, such as radius, ellipticity, and the rotational energy budget of pulsars, which could explain the X-ray luminosity of some sources. Finally, we also show that non-rigidity weakens the universal $I$-Love-$Q$ relations., Comment: 12 pages, 5 figures. Accepted for publication in PRD

A Newtonian-like theory inspired by the Brans-Dicke gravitational Lagrangian has been recently proposed. For static configurations the gravitational coupling acquires an intrinsic spatial dependence within the matter distribution. Therefore, the interior of astrophysical configurations may provide a testable environment for this approach as long as no screening mechanism is evoked. In this work we focus on the stellar hydrostatic equilibrium structure in such varying $G$ scenario. A modified Lane-Emden equation is presented and its solutions for various values of the polytropic index are discussed. The role played by the theory parameter $\omega$, the analogue of the Brans-Dicke parameter, on the physical properties of stars is discussed., Comment: 6 pages, 4 figures

Pulsar-timing has become a celebrated tool for probing modifications to General Relativity in the strong-field surroundings of neutron stars. Here we investigate whether scalar-tensor theories that incorporate a nonminimally coupled scalar degree of freedom may pass pulsar-timing tests, by computing the scalar charges entering such observables. In particular we show that for positive values of the nonminimal coupling $\xi$, pulsar-timing constraints may be evaded even in the presence of spontaneous scalarization., Comment: 12 pages, 6 figures