  The Lense-Thirring effect from spinning neutron stars in double neutron star
binaries contribute to the periastron advance of the orbit. This extra term
involves the moment of inertia of the neutron stars. Moment of inertia, on the
other hand, depends on the mass and spin of the neutron star as well as the
equation of state of the matter. If at least one member of the double neutron
star binary (better the faster one) is a radio pulsar, then accurate timing
analysis might lead to the estimation of the contribution of the Lense-Thirring
effect to the periastron advance, which will lead to the measurement of the
moment of inertia of the pulsar. Combination of the knowledge on the values of
the moment of inertia, the mass, and the spin of the pulsar, will give a new
constraint on the equation of state. Pulsars in double neutron star binaries
are the best for this purpose as short orbits and moderately high
eccentricities make the Lense-Thirring effect substantial, whereas tidal
effects are negligible (unlike pulsars with main sequence or white-dwarf
binaries). The most promising pulsars are PSR J0737-3039A and PSR J1757-1854.
The spin-precession of pulsars due to the misalignment between the spin and the
orbital angular momentum vectors affect the contribution of the Lense-Thirring
effect to the periastron advance. This effect has been explored for both PSR
J0737-3039A and PSR J1757-1854, and as the misalignment angles for both of
these pulsars are small, the variation in the Lense-Thirring term is not much.
However, to extract the Lense-Thirring effect from the observed rate of the
periastron advance, more accurate timing solutions including precise proper
motion and distance measurements are essential.
