Classical general relativity effects by magnetars with massive quadrupole, angular momentum and a magnetic dipole

In this contribution, we obtain classical tests of general relativity using the Hartle-Thorne metric endowed with magnetic dipole and electric charge. This metric represents the approximate stationary spacetime of a massive object with the other characteristics mentioned. These tests are light deflection, time delay, peri-astron precession, and gravitational redshift. We also provide numerical estimates for real magnetars and magnetar candidates from the McGill magnetar catalog, the millisecond pulsar PSR B1257+12 and for the Sun in low-activity cycles. Our results find that, although the magnetic dipole moment contribution tends to be negligible compared to the total amount, its comparison to the massive quadrupole moment and rotational contributions varies from one classical test to the next. For light deflection, the magnetic dipole contribution is about 2 orders of magnitude smaller, compared to the rotational contribution. The magnetic dipole moment contribution is present, but is about 6 orders of magnitude smaller than the second-order rotational contribution to the periastron precession, 5 orders of magnitude smaller for the time delay, and negligible within the approximation presented for the gravitational redshift. The magnetic dipole contribution 1 for the calculations made with PSR B1257+12 was also negligible, but the rotational and quadrupole moment contributions were more significant, which makes the argument for possible future detection stronger than the magnetar case. The rotation, massive quadrupole moment and magnetic dipole contributions for the Sun turned out to be negligible as well.