https://doi.org/10.1140/epjc/s10052-017-5008-1
Regular Article - Theoretical Physics
Post-Keplerian perturbations of the orbital time shift in binary pulsars: an analytical formulation with applications to the galactic center
Ministero dell’Istruzione, dell’Università e della Ricerca (M.I.U.R.)-Istruzione, Viale Unità di Italia 68, 70125, Bari, BA, Italy
* e-mail: lorenzo.iorio@libero.it
Received:
27
March
2017
Accepted:
21
June
2017
Published online:
1
July
2017
We develop a general approach to analytically calculate the perturbations 
of the orbital component of the change 
of the times of arrival of the pulses emitted by a binary pulsar p induced by the post-Keplerian accelerations due to the mass quadrupole 
, and the post-Newtonian gravitoelectric (GE) and Lense–Thirring (LT) fields. We apply our results to the so-far still hypothetical scenario involving a pulsar orbiting the supermassive black hole in the galactic center at Sgr A
. We also evaluate the gravitomagnetic and quadrupolar Shapiro-like propagation delays 
. By assuming the orbit of the existing main sequence star S2 and a time span as long as its orbital period 
, we obtain 
. Faster 
and more eccentric 
orbits would imply net shifts per revolution as large as 
, depending on the other orbital parameters and the initial epoch. For the propagation delays, we have 
. The results for the mass quadrupole and the Lense–Thirring field depend, among other things, on the spatial orientation of the spin axis of the Black Hole. The expected precision in pulsar timing in Sgr A is of the order of 
, or, perhaps, even 1–10 
. Our method is, in principle, neither limited just to some particular orbital configuration nor to the dynamical effects considered in the present study.
© The Author(s), 2017
