1002.3399 (M. I. Wanas et al.)

On the Field of a Binary Pulsar    [PDF]

M. I. Wanas, N. S. Awadalla, W. S. El Hanafy

In the present work, the exact solution of Einstein's field equations which has been given by Curzon in 1924 representing the field of a static binary system is reviewed. An adapted version of this solution is obtained to describe a dynamical binaries in a rotating coordinate system. It is shown that this version of the solution is time-dependent one. It reduces to the later one in the static case if the rotation goes to zero. The original Curzon solution shows that there are two singularities at the two masses, while in the modified version the singularities become on the world-line of the two masses. The solution shows no additional coordinate singularities. The killing vector field of the axial symmetry is obtained in the modified version. In addition the rotation admits a further rotational symmetry, so a rotation killing vector field is also obtained and discussed. The equations of motion for a test particle in the field of a binary system are formulated and solved. Such equations has been used to study the gravitational time delay of arrival (Shapiro delay) of signals from binary pulsar systems resulted from our suggested modifications containing additional terms. These terms are interpreted as corrections due to gravitomagnetic effect of the orbital angular motion of the double pulsars, second and third order in the mass of the companion. In particular, we investigate the time delay in the case of the double-pulsar system PSR J0737-3039 A/B. We give numerical estimates of the gravitomagnetic contribution for the time delay of this system.

View original: http://arxiv.org/abs/1002.3399