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In the last few decades, lots of universal relations between different globalphysical quantities of neutron stars have been proposed to constrain theunobservable or hard to be observed properties of neutron stars. But few ofthem are related to the gravitational redshift or the gravitational bindingenergy, especially for the fast rotating neutron stars. Here we will focus onthe universal relations related to these two quantities. Based on 11 equationsof state (EOSs) from the predictions of microscopic nuclear many-body theoriesfor normal or hybrid neutron stars, we proposed a set of new quasi-universalrelations under three rotating cases: static, general rotating and Keplerianrotating. These new quasi-universal relations provide a potential way toconstrain or estimate the unobservable or hard to be observed properties ofneutron stars.

New quasi-universal relations for static and rapid rotating neutron stars