IJAA  Vol.6 No.3 , September 2016
Approximate Kerr-Like Metric with Quadrupole
Abstract: A new approximate metric representing the spacetime of a rotating deformed body is obtained by perturbing the Kerr metric to include up to the second order of the quadrupole moment. It has a simple form, because it is Kerr-like. Its Taylor expansion form coincides with second order quadrupole metrics with slow rotation already found. Moreover, it can be transformed to an improved Hartle-Thorne metric, which guarantees its validity to be useful in studying compact object, and it is possible to find an inner solution.
Cite this paper: Frutos-Alfaro, F. (2016) Approximate Kerr-Like Metric with Quadrupole. International Journal of Astronomy and Astrophysics, 6, 334-345. doi: 10.4236/ijaa.2016.63028.

[1]   Hernández, W. (1967) Material Sources for the Kerr Metric. Physical Review, 159, 1070-1072.

[2]   Thorne, K.S. (1980) Multipole Expansions of Gravitational Radiation. Reviews on Modern Physics, 52, 299-340.

[3]   Ernst, F.J. (1968) New Formulation of the Axially Symmetric Gravitational Field Problem. Physical Review, 167, 1175-1177.

[4]   Hoenselaers, C., Kinnersley, W. and Xanthopoulos, B.C. (1979) Symmetries of the Stationary Einstein-Maxwell Equations. VI. Transformations Which Generate Asymptotically Flat Spacetimes with Arbitrary Multipole Moments. Journal of Mathematical Physics, 20, 2530-2536.

[5]   Carmeli, M. (2001) Classical Fields: General Relativity and Gauge Theory. World Scientific Publishing, Singapore.

[6]   Frutos-Alfaro, F., Retana-Montenegro, E., Cordero-Garca, I. and Bonatti-González, J. (2013) Metric of a Slow Rotating Body with Quadrupole Moment from the Erez-Rosen Metric. International Journal of Astronomy and Astrophysics, 3, 431-437.

[7]   Frutos-Alfaro, F., Montero-Camacho, P., Araya, M. and Bonatti-González, J. (2015) Approximate Metric for a Rotating Deformed Mass. International Journal of Astronomy and Astrophysics, 5, 1-10.

[8]   Montero-Camacho, P., Frutos-Alfaro, F. and Gutiérrez-Chaves, C. (2015) Slowly Rotating Curzon-Chazy Metric. Revista de Matemática (Teora y Aplicaciones), 22, 265-274.

[9]   Hartle, J.B. and Thorne, K.S. (1968) Slowly Rotating Relativistic Stars. II. Models for Neutron Stars and Supermassive Stars. Astrophysical Journal, 153, 807-834.

[10]   Quevedo, H. (2011) Exterior and Interior Metrics with Quadrupole Moment. General Relativity and Gravitation, 43, 1141-1152.

[11]   Boshkayev, K., Quevedo, H. and Ruffini, R. (2012) Gravitational Field of Compact Objects in General Relativity. Physical Review D, 86, Article ID: 064043.

[12]   Quevedo, H. and Mashhoon, B. (1991) Generalization of Kerr Spacetime. Physical Review, 43, 3902-3906.

[13]   Manko, V.S. and Novikov, I.D. (1992) Generalizations of the Kerr and Kerr-Newman Metrics Possessing an Arbitrary Set of Mass-Multipole Moments. Classical and Quantum Gravity, 9, 2477-2487.

[14]   Frutos-Alfaro, F., Grave, F., Müeller, T. and Adis, D. (2012) Wavefronts and Light Cones for Kerr Spacetimes. Journal of Modern Physics, 3, 1882-1890.

[15]   Hearn, A.C. (1999) REDUCE (User’s and Contributed Packages Manual). Konrad-Zuse-Zentrum für Informationstechnik, Berlin.

[16]   Frutos-Alfaro, F. and Soffel, M. (2015) On the Post-Linear Quadrupole-Quadrupole Metric.

[17]   Fodor, G., Hoenselaers, C. and Perjés, Z. (1989) Multipole Moments of Axisymmetric Systems in Relativity. Journal of Mathematical Physics, 30, 2252-2257.

[18]   Frutos-Alfaro, F. and Soffel, M. (2016) Multipole Moments of the Generalized Quevedo-Mashhoon Metric.