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

TL;DR

This paper reviews and modifies Curzon's static binary gravitational field solution to include dynamical, rotating effects, and studies their impact on pulsar signal timing, especially the gravitational time delay in binary pulsar systems.

Contribution

It introduces a time-dependent, rotating binary system solution to Einstein's equations and analyzes its effects on pulsar timing, including higher order corrections and gravito-magnetic effects.

Findings

Modified solution describes dynamical binary systems with no additional singularities.

Derived equations of motion used to compute gravitational time delay effects.

Numerical estimates show significant gravito-magnetic contributions in pulsar timing.

Abstract

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. 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 have 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 higher order corrections to the masses. In particular we investigate the gravito-magnetic effect due to orbital angular motion of the double pulsars. We give numerical estimates of this type of the time delay in the case of the double-pulsar system PSR J0737-3039 A/B. We draw a model curve for the gravito-magnetic time delay during one orbital revolution. We suggest that this type of delay will have a larger contribution during the last phase of the system evolution.