Neutron stars (NSs) are excellent laboratories for testing gravity theories as they are strongly self-gravitating bodies and have rich observational phenomena. However, strong-field gravity effects in NSs could be degenerate with their equation of state (EOS) which is largely unknown. Fortunately, there exist the so-called universal relations among the NS macroscopic quantities that are found to be insensitive to the underlying EOS. Studying the origin of these relations can lead to a better understanding of NSs and the gravitational interaction. We develop a new perspective of view to analyze the $I\text{−}C$ and $I$-Love universal relations for NSs. At the linear order, we separate the deviation of the universal relations into two factors that are multiplied together. One is the EOS difference, while the other factor only depends on the background star structure. The smallness of the second factor that does not depend on the EOS difference then indicates the origin of the universality. We discuss the validity of our linear approximation when considering the difference among realistic EOS. Our study can be regarded as a new frame for quantitative representation of the universality and may provide new insights to the universal relations of NSs.

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• General relativity
• Neutron stars & pulsars