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In the present work, the exact solution of Einstein's field equations whichhas been given by Curzon in 1924 representing the field of a static binarysystem is reviewed. An adapted version of this solution is obtained to describea dynamical binaries in a rotating coordinate system. It is shown that thisversion of the solution is time-dependent. It reduces to the later one in thestatic case if the rotation goes to zero. The original Curzon solution showsthat there are two singularities at the two masses, while in the modifiedversion the singularities become on the world-line of the two masses. Thesolution shows no additional coordinate singularities. The killing vector fieldof the axial symmetry is obtained in the modified version. In addition, therotation admits a further rotational symmetry, so a rotation killing vectorfield is also obtained and discussed. The equations of motion for a testparticle in the field of a binary system are formulated and solved. Suchequations have been used to study the gravitational time delay of arrival(Shapiro delay) of signals from binary pulsar systems resulted from oursuggested modifications containing additional terms. These terms areinterpreted as higher order corrections to the masses. In particular weinvestigate the gravito-magnetic effect due to orbital angular motion of thedouble pulsars. We give numerical estimates of this type of the time delay inthe case of the double-pulsar system PSR J0737-3039 A/B. We draw a model curvefor the gravito-magnetic time delay during one orbital revolution. We suggestthat this type of delay will have a larger contribution during the last phaseof the system evolution.

Strong Field of Binary Systems And Its Effects On Pulsar Arrival Times