With a selected sample of neutron star ( NS ) equation-of-states ( EOSs ) that are consistent with the current observations and have a range of maximum masses , we investigate the relations between NS gravitational mass M _ { g } and baryonic mass M _ { b } , and the relations between the maximum NS mass supported through uniform rotation ( M _ { max } ) and that of nonrotating NSs ( M _ { TOV } ) .
We find that if one intends to apply an EOS-independent quadratic , universal transformation formula ( M _ { b } = M _ { g } + A \times M _ { g } ^ { 2 } ) to all EOSs , the best fit A value is 0.080 for non-rotating NSs only and 0.073 when different spin periods are considered .
The residual error of the transformation is as large as \sim 0.1 M _ { \odot } .
For different EOSs , we find that the parameter A for non-rotating NSs is proportional to R _ { 1.4 } ^ { -1 } ( where R _ { 1.4 } is NS radius for 1.4 M _ { \odot } in unit of km ) .
For a particular EOS , if one adopts the best-fit parameters for different spin periods , the residual error of the transformation is smaller , which is of the order of 0.01 M _ { \odot } for the quadratic form and less than 0.01 M _ { \odot } for the cubic form ( M _ { b } = M _ { g } + A _ { 1 } \times M _ { g } ^ { 2 } + A _ { 2 } \times M _ { g } ^ { 3 } ) .
We also find a very tight and general correlation between the normalized mass gain due to spin \Delta m \equiv ( M _ { max } - M _ { TOV } ) / M _ { TOV } and the spin period normalized to the Keplerian period { \cal P } , i.e . { log _ { 10 } } \Delta m = ( -2.74 \pm 0.05 ) { log _ { 10 } } { \cal P } + { log _ { 10 } } ( 0. % 20 \pm 0.01 ) , which is independent of EOS models .
Applications of our results to GW170817 is discussed .