https://doi.org/10.1140/epjc/s10052-019-7238-x
Regular Article - Theoretical Physics
Effective apsidal precession from a monopole solution in a Zipoy spacetime
1
Applied Physics Graduation Program, UNILA, Foz do Iguaçu, PR, 85867-670, Brazil
2
Universidade Federal do Tocantins, Curso de Física, Setor Cimba, Araguaína, TO, 77824-838, Brazil
* e-mail: abecapistrano@gmail.com
Received:
11
July
2019
Accepted:
20
August
2019
Published online:
30
August
2019
In this work, we examine the orbit equations originated from Zipoy’s oblate metric. Accordingly, the solution of Einstein’s vacuum equations can be written as a linear combination of Legendre polynomials of positive definite integers l. Starting from the zeroth order 
, in a nearly newtonian regime, we obtain a non-trivial formula favoring both retrograde and advanced solutions for the apsidal precession, depending on parameters related to the metric coefficients. Using a Chi-squared statistics, we apply the model to the apsidal precessions of Mercury and asteroids (1566 Icarus and 2-Pallas). As a result, we show that the obtained values favor the oblate solution as a more adapted approach as compared to those results produced by Weyl’s cylindric and Schwarzschild solutions. Moreover, it is also shown that the resulting solution converges to the integrable case 
in the sense of the Zipoy–Voorhees metric.
© The Author(s), 2019
