Effective apsidal precession from a monopole solution in a Zipoy spacetime
Abstract 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 $$l=0$$ l=0 , in a near...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-08-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | http://link.springer.com/article/10.1140/epjc/s10052-019-7238-x |
| _version_ | 1818335168580026368 |
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| author | Abraão J. S. Capistrano Paola T. Z. Seidel Luís A. Cabral |
| author_facet | Abraão J. S. Capistrano Paola T. Z. Seidel Luís A. Cabral |
| author_sort | Abraão J. S. Capistrano |
| collection | DOAJ |
| description | Abstract 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 $$l=0$$ l=0 , 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 $$\gamma =1$$ γ=1 in the sense of the Zipoy–Voorhees metric. |
| first_indexed | 2024-12-13T14:19:08Z |
| format | Article |
| id | doaj.art-79a9f4bea4e84270a46e20b03bd2b697 |
| institution | Directory Open Access Journal |
| issn | 1434-6044 1434-6052 |
| language | English |
| last_indexed | 2024-12-13T14:19:08Z |
| publishDate | 2019-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj.art-79a9f4bea4e84270a46e20b03bd2b6972022-12-21T23:42:09ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60441434-60522019-08-017991810.1140/epjc/s10052-019-7238-xEffective apsidal precession from a monopole solution in a Zipoy spacetimeAbraão J. S. Capistrano0Paola T. Z. Seidel1Luís A. Cabral2Applied Physics Graduation Program, UNILAApplied Physics Graduation Program, UNILAUniversidade Federal do Tocantins, Curso de FísicaAbstract 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 $$l=0$$ l=0 , 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 $$\gamma =1$$ γ=1 in the sense of the Zipoy–Voorhees metric.http://link.springer.com/article/10.1140/epjc/s10052-019-7238-x |
| spellingShingle | Abraão J. S. Capistrano Paola T. Z. Seidel Luís A. Cabral Effective apsidal precession from a monopole solution in a Zipoy spacetime European Physical Journal C: Particles and Fields |
| title | Effective apsidal precession from a monopole solution in a Zipoy spacetime |
| title_full | Effective apsidal precession from a monopole solution in a Zipoy spacetime |
| title_fullStr | Effective apsidal precession from a monopole solution in a Zipoy spacetime |
| title_full_unstemmed | Effective apsidal precession from a monopole solution in a Zipoy spacetime |
| title_short | Effective apsidal precession from a monopole solution in a Zipoy spacetime |
| title_sort | effective apsidal precession from a monopole solution in a zipoy spacetime |
| url | http://link.springer.com/article/10.1140/epjc/s10052-019-7238-x |
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