Multipole structure of compact objects

  • H. Quevedo Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, AP 70543, México, DF 04510, Mexico Dipartimento di Fisica and ICRA, Università di Roma "La Sapienza", I-00185 Roma

Abstract

We analyze the applications of general relativity in relativistic astrophysics in order to solve the problem of describing the geometric and physical properties of the interior and exterior gravitational and electromagnetic fields of compact objects. We focus on the interpretation of exact solutions of Einstein's equations in terms of their multipole moments structure. In view of the lack of physical interior solutions, we propose an alternative approach in which higher multipoles should be taken into account.

References

[1] A. Einstein. Die Feldgleichungen der Gravitation. –Sitzungsberichte der Preussischen Akademie der Wissenschaften: Berlin, 1915. – P. 844-847.
[2] H. Stephani, D. Kramer, M. A. H. MacCallum, C. Hoenselaers, and E. Herlt. Exact Solutions of Einstein's Field Equations. – Cambridge University Press: Cambridge, UK, 2003.
[3] H. Quevedo. Multipolar solutions, in Cosmology and Gravitatio // Proceedings of the XIVth Brazilian School of Cosmology and Gravitation, edited M. Novello and S. E. Perez Bergliaffa. – Cambridge Scientific Publishers, 2011. – P. 83-97.
[4] D. Pugliese, H. Quevedo and R. Ruffini. Equa-torial circular orbits of neutral test particles in the Kerr-Newman spacetime. Equatorial circular orbits of neutral test particles in the Kerr-Newman spacetime // Phys. Rev. D –2013.– Vol. 88. – P. 024042.
[5] R. Geroch. Multipole moments. I. Flat space // J.Math. Phys. – 1970. – Vol. 11. – P. 1955-1960;Multipole moments. II. Curved space // J. Math. Phys. – 1970. – Vol. 11. – P. 2580-2588.
[6] R. O. Hansen. Multipole moments of stationary spacetimes // J. Math. Phys. 1974. – Vol. 15. – P. 46-52.
[7] H. Quevedo. Multipole Moments in General Relativity -Static and Stationary Solutions // Fort. Phys. – 1990. – Vol. 38. – P. 733-840.
[8] H. Quevedo. Generating Solutions of the Einstein - Maxwell Equations with Prescribed Physical Properties // Phys. Rev. D. – 1992. – Vol. 45. – P. 1174-1177.
[9] R. P. Kerr. Gravitational field of a spinning mass as an example of algebraically special metrics // Phys. Rev. Lett. – 1963. – Vol. 11. – P. 237-238.
[10] M. Heusler. Black Hole Uniqueness Theorems. – Cambridge University Press: Cambridge, UK, 1996. – 264 p.
[11] H. Weyl. Zur Gravitationstheorie // Ann. Physik. – 1917. – Vol. 54. – P. 117-145.
[12] G. Erez and N. Rosen. The gravitational field of a particle possessing a quadrupole moment // Bull. Res. Counc. Israel. – 1959. – Vol.8F. – P. 47-50.
[13] A. Tomimatsu and H. Sato. New series of exact solutions for gravitational fields of spinning masses // Prog. Theor. Phys. – 1973. – Vol. 50. – P. 95-110.
[14] T.I. Gutsunaev, V.S. Manko. On the gravitational field of a mass possessing a multipole moment // Gen. Rel. Grav. – 1985. – Vol. 17. – P. 1025-1027.
[15] H. Quevedo. On the exterior gravitational field of a mass with a multipole moment // Gen. Rel. Grav. – 1987. – Vol. 19. – P. 1013 - 1023.
[16] H. Quevedo. Exterior and interior metrics with quadrupole moment // Gen. Rel. Grav. – 2011. – Vol. 43. – P. 1141-1152.
[17] D. M. Zipoy. Topology of some spheroidal metrics // J. Math. Phys. 1966. – Vol. 7. – P. 1137-1143.
[18] B. Voorhees. Static axially symmetric gravitational fields // Phys. Rev. D. – 1970. – Vol. 2. – P. 2119-2122.
[19] H. Quevedo. General static axisymmetric solution of Einstein's vacuum field equations in prolate spheroidal coordinates // Phys. Rev. D. – 1989. – Vol. 39. – P. 2904-2911.
[20] H. Quevedo and B. Mashhoon. Exterior gravitational field of a rotating deformed mass // Phys. Lett. A. – 1985. – Vol. 109. – P. 13-18.
[21] V.S.Manko and I.D. Novikov. Class //Quantum Grav. – 9, 2477 (1992).
[22] J. Castejon-Amenedo and V.S. Manko.On a stationary rotating mass with an arbitrary multipole structure //Class. Quantum Grav. – 1990. – Vol. 7. – P. 779-785.
[23] H. Quevedo and B. Mashhoon. Generalization of Kerr spacetime // Phys. Rev. D. 1991. – Vol. 43. – P. 3902-3906.
[24] V.S. Manko, E. Mielke, J.D. Sanabria. Exact solution for the exterior field of a rotating neutron star // Phys. Rev. D. – 2000. – Vol. 61. – P. 081501.
[25] L. Pachón, J.A. Rueda, J.D. Sanabria.Realistic exact solution for the exterior field of a rotating neutron star// Phys. Rev. D. 2006. – Vol. 73. – P. 104038.
[26] A. Gutiérrez-Piñeres, G. González and H. Quevedo.Conformastatic disk-haloes in Einstein-Maxwell gravity // Phys. Rev. D.–2013. – Vol. 87. – P. 044010.
[27] H. Quevedo and S. Toktarbay. Generating static perfect-fluid solutions of Einstein's equations //J. Math. Phys. – 2015. – Vol. 56. – P. 052502.
Published
2017-03-06
How to Cite
QUEVEDO, H.. Multipole structure of compact objects. Physical Sciences and Technology, [S.l.], v. 3, n. 1, mar. 2017. ISSN 2409-6121. Available at: <http://phst.kaznu.kz/index.php/journal/article/view/93>. Date accessed: 13 dec. 2017.
Section
Theoretical Physics and Astrophysics

Keywords

Exact solutions of Einstein equations, compact objects, multipole moments