Abstract The universal relations in neutron stars form an essential entity to understand their properties. The moment of inertia, dimensionless tidal deformability, mass quadrupole moment, and oscillation modes are some of the properties that have been studied previously in the context of universal relations. All of these quantities are measurable; thus, analyzing them is of utmost importance. In this article we provide new universal relations in the context of a neutron star’s gravitational redshift. Using the redshift measurements of RBS 1223, RX J0720.4-3125, and RX J1856.5-3754, we provide theoretical estimates of moment of inertia, dimensionless tidal deformability, mass quadrupole moment, the mass of the star times the ratio of angular frequency over the spin angular moment, and the average of the speed of sound squared. In the case of the redshift measurement of RX J0720.4-3125, we found that the theoretical estimate using universal relations aligns closely with the Bayesian estimate. Our findings indicate that such theoretical predictions are highly reliable for observations with low uncertainty and can be used as an alternative for statistical analysis. Additionally, we report a violation of the universality of the dimensionless tidal deformability and average of the speed of sound squared with respect to the gravitational redshift. Our calculations further indicate that, under current astrophysical constraints, the maximum gravitational redshift attainable by neutron stars does not exceed 0.763.
Chatterjee et al. (Mon,) studied this question.