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Metric of a Slow Rotating Body with Quadrupole Moment from the Erez-Rosen Metric
School of Physics, University of Costa Rica, San Pedro, Costa Rica
School of Physics, University of Costa Rica, San Pedro, Costa Rica
School of Physics, University of Costa Rica, San Pedro, Costa Rica
School of Physics, University of Costa Rica, San Pedro, Costa Rica
- 1 School of Physics, University of Costa Rica, San Pedro, Costa Rica
- 2 School of Physics, University of Costa Rica, San Pedro, Costa Rica
- 3 School of Physics, University of Costa Rica, San Pedro, Costa Rica
- 4 School of Physics, University of Costa Rica, San Pedro, Costa Rica
International Journal of Astronomy and Astrophysics·Volume 03 (2013)·Pages 431–437·Published 9 October 2013·DOI10.4236/ijaa.2013.34051
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Abstract
A metric representing a slowly rotating object with quadrupole moment is obtained using a perturbation method to include rotation into the weak limit of the Erez-Rosen metric. This metric is intended to tackle relativistic astrometry and gravitational lensing problems in which a quadrupole moment has to be taken into account.
KeywordsGeneral RelativityEinstein Field EquationsQuadrupole MomentErez-Rosen Metric
- G. Erez and N. Rosen, “The Gravitational Field of a Particle Possessing a Multipole Moment,” Bulletin of the Research Council of Israel, Vol. 8F, 1959, pp. 47-50.
- A. G. Doroshkevich, Ya. B. Zel’dovich and I. D. Novikov, “Gravitational Collapse of Nonsymmetric and Rotating Masses,” Journal of Experimental and Theoretical Physics (Soviet Physics JETP), Vol. 22, No. 1, 1966, pp. 122-130. http://www.jetp.ac.ru/cgi-bin/e/index/e/22/1/p122?a=list
- J. Winicour, A. I. Janis and E. T. Newman, “Static, Axially Symmetric Point Horizons,” Physical Review, Vol. 176, No. 5, 1968, pp. 1507-1513. http://dx.doi.org/10.1103/PhysRev.176.1507
- J. H. Young and C. A. Coulter, “Exact Metric for a Nonrotating Mass with a Quadrupole Moment,” Physical Review, Vol. 184, No. 5, 1969, pp. 1313-1315. http://dx.doi.org/10.1103/PhysRev.184.1313
- H. Quevedo, “Class of Stationary Axisymmetric Solutions of Einstein’s Equations in Empty Space,” Physical Review D, Vol. 33, No. 2, 1986, pp. 324-327. http://dx.doi.org/10.1103/PhysRevD.33.324
- H. Quevedo, “General Static Axisymmetric Solution of Einstein’s Vacuum Field Equations in Prolate Spheroidal Coordinates,” Physical Review D, Vol. 39, No. 10, 1989, pp. 2904-2911. http://dx.doi.org/ 10.1103/PhysRevD.39.2904
- H. Quevedo and B. Mashhoon, “Generalization of Kerr Spacetime,” Physical Review D, Vol. 43, No. 12, 1991, pp. 3902-3906. http://dx.doi.org/10.1103/PhysRevD.43.3902
- J. Castejon-Amenedo and V. S. Manko, “Superposition of the Kerr Metric with the Generalized Erez-Rosen Solution,” Physical Review D, Vol. 41, No. 6, 1990, pp. 2018-2020. http://dx.doi.org/10. 1103/PhysRevD.41.2018
- C. Hoenselaers, W. Kinnersley and B. C. Xanthopoulos, “Symmetries of the Stationary Einstein-Maxwell Equations. VI. Transformations which generate Asymptotically Flat Spacetimes with Arbitrary Multipole Moments,” Journal of Mathematical Physics, Vol. 20, No. 12, 1979, pp. 2530-2536. http://dx.doi.org/10.1063/1.524058
- F. J. Ernst, “New Formulation of the Axially Symmetric Gravitational Field Problem,” Physical Review, Vol. 167, No. 5, 1968, pp. 1175-1177. http://dx.doi.org/10.1103/PhysRev.167.1175
- K. Boshkayev, H. Quevedo and R. Ruffini, “Gravitational Field of Compact Objects in General Relativity,” Physical Review D, Vol. 86, No. 6, 2012, Article ID: 064043. http://dx.doi.org/10. 1103/PhysRevD.86.064043
- A. C. Hearn, “REDUCE (User’s and Contributed Packages Manual),” Konrad-Zuse-Zentrum für Informationstechnik, Berlin, 1999. http://reduce-algebra.com/