English (pdf)
Article in xml format
Article references
Automatic translation
Send this article by e-mail
Permalink
Mathematics Subject Classification: 83C05, 83C25, 85-02.
Ver contenido completo en PDF.
Services on Demand
Journal
Article
Indicators
-
Cited by SciELO -
Access statistics
Related links
-
Similars in
SciELO
Share
Revista de Matemática Teoría y Aplicaciones
Print version ISSN 1409-2433
Rev. Mat vol.28 n.2 San José Jul./Dec. 2021
http://dx.doi.org/10.15517/rmta.v28i2.37152
Artículo
Approximate Kerr-Newman-like metric with quadrupole
Métrica aproximada tipo Kerr-Newman con cuadrupolo
1Universidad de Costa Rica, Escuela de Física, Centro de Investigaciones Espaciales (CINESPA), San José, Costa Rica; francisco.frutos@ucr.ac.cr
2Universidad de Costa Rica, Escuela de Física, Centro de Investigaciones Espaciales (CINESPA), San José, Costa Rica; pedro.gomezovares@gmail.com
3Tsinghua University, Department of Astronomy, Beijing, China; pmontero@tsinghua.edu.cn
The Kerr metric is known to have issues when trying to find a physical interior solution. In this work we continue our efforts to construct a more realistic exterior metric for astrophysical objects. A new approximate metric representing the spacetime of a charged, rotating and slightly-deformed body is obtained by perturbing the Kerr-Newman metric to include the mass-quadrupole and quadrupole-quadrupole orders. It has a simple form because it is Kerr-Newman-like.
Keywords: general relativity; solutions of Einstein’s equations; approximation procedures; weak fields.
Se sabe que la métrica de Kerr tiene problemas al tratar de encontrar una solución física interior. En este trabajo continuamos nuestros esfuerzos para construir una métrica exterior más realista para describir objetos astrofísicos. Una nueva métrica aproximada que representa el espaciotiempo de un cuerpo cargado, giratorio y ligeramente deformado, se obtiene perturbando la métrica de Kerr-Newman para incluir los órdenes de masa-cuadrupolo y cuadrupolo-cuadrupolo. Tiene una forma simple porque es similar a Kerr-Newman.
Palabras clave: relatividad general; soluciones de las ecuaciones de Einstein; procedimientos de aproximación; campos débiles.
Acknowledgements
Thanks to the referees for their constructive and valuable observations that allowed an improvement of the manuscript.
References
K, Boshkayev; H, Quevedo; R, Ruffini. Gravitational field of compact objects in general relativity, Physical Review D 86(2012), no. 6, 064043. Doi: 10.1103/PhysRevD.86.064043 [ Links ]
M, Carmeli. Classical Fields: General Relativity and Gauge Theory, World Scientific Publishing Company, Singapore, 2001. Doi: 10.1142/4843 [ Links ]
S, Chandrasekhar. The Mathematical Theory of Black Holes, Clarendon Press, Oxford, 1998. [ Links ]
J,E, Cuchí; A, Molina; E, Ruiz. Double shell stars as source of the Kerr metric in the CMMR approximation, Journal of Physics: Conference Series 314(2011), 012070. Doi: 10.1088/1742-6596/314/1/012070 [ Links ]
S,P, Drake; R, Turolla. The application of the Newman-Janis algorithm in obtaining interior solutions of the Kerr metric, Classical and Quantum Gravity 14(1997), 1883-1897. Doi: 10.1088/0264-9381/14/7/021 [ Links ]
E,F, Eiroa; G,E, Romero; D,F, Torres. Reissner-Nordström black hole lensing, Physical Review D 66(2002), 024010. Doi: 10.1103/PhysRevD.66.024010 [ Links ]
F, J, Ernst. New formulation of the axially symmetric gravitational field problem, Physical Review 167(1968), no. 5, 1175-1177. Doi: 10.1103/PhysRev.167.1175 [ Links ]
F, J , Ernst. New formulation of the axially symmetric gravitational field problem. II, Physical Review 168(1986), no. 5, 1415-1417. Doi: 10.1103/PhysRev.168.1415 [ Links ]
G, Fodor; C, Hoenselaers; Z, Perjés. Multipole moments of axisymmetric systems in relativity, Journal of Mathematical Physics 30(1989), no. 10, 2252-2257. Doi: 10.1063/1.528551 [ Links ]
F, Frutos-Alfaro. Approximate Kerr-like metric with quadrupole, International Journal of Astronomy and Astrophysics 6(2016), no. 3, 334-345. Doi: 10.4236/ijaa.2016.63028 [ Links ]
F, Frutos-Alfaro; P, Montero-Camacho; M, Araya; J, Bonatti-González. Approximate metric for a rotating deformed mass, International Journal of Astronomy and Astrophysics 5(2015), no. 1, 1-10. Doi: 10.4236/ijaa.2015.51001 [ Links ]
F, Frutos-Alfaro; E, Retana-Montenegro; I, Cordero-García; J, Bonatti-González. Metric of a slow rotating body with quadrupole moment from the Erez-Rosen metric, International Journal of Astronomy and Astrophysics 3(2013), no. 4, 431-437. Doi: 10.4236/ijaa.2013.34051 [ Links ]
F, Frutos-Alfaro; M, Soffel. On the post-linear quadrupole-quadrupole metric, Revista de Matemática: Teoría y Aplicaciones 24(2017), no. 2, 239-255. Doi: 10.15517/rmta.v24i2.29856 [ Links ]
S, Haggag. A static axisymmetric anisotropic fluid solution in general relativity, Astrophysics and Space Science 173(1990), no. 1, 47-51. Doi: 10.1007/BF00642561 [ Links ]
J,B, Hartle; K,S, Thorne. Slowly rotating relativistic stars. II. Models for neutron stars and supermassive stars, Astrophysical Journal 153(1968), 807-834. Doi: 10.1086/149707 [ Links ]
A,C,Hearn.REDUCE (User’s and Contributed Packages Manual), Konrad-Zuse-Zentrum für Informationstechnik, Berlin, 1999. [ Links ]
J,L, Hernández-Pastora; L, Herrera. Interior solution for the Kerr metric, Physical Review D 95(2017), no. 2, 024003. Doi: 10.1103/PhysRevD.95.024003 [ Links ]
C, Hoenselaers; Z, Perjés. Multipole moments of axisymmetric electrovacuum spacetimes, Classical and Quantum Gravity 7(1990), no.10, 1819-1825. Doi: 10.1088/0264-9381/7/10/012 [ Links ]
R,P,Kerr.Gravitational field of a spinning mass as an example of algebraically special metrics, Physical Review Letters 11(1963), no. 5, 237-238. Doi: 10.1103/PhysRevLett.11.237 [ Links ]
W, Kinnersley. Type D vacuum metrics, Journal of Mathematical Physics 10(1969), no. 7, 1195-1203. Doi: 10.1063/1.1664958 [ Links ]
A, Krasinski. A newtonian model of the source of the Kerr metric, Physics Letters A 80(1980), no. 4, 238-242. Doi: 10.1016/0375-9601(80)90010-9 [ Links ]
J,P, Krisch; E,N, Glass. Counter-rotating Kerr manifolds separated by a fluid shell, Classical and Quantum Gravity 26(2009), no. 17, 175010. Doi: 10.1088/0264-9381/26/17/175010 [ Links ]
F,W, Letniowski; R,G, McLenaghan. An improved algorithm for quartic equation classification and petrov classification, General Relativity and Gravitation 20(1988), no. 5, 463-483. Doi: 10.1007/BF00758122 [ Links ]
F,Z,Majidi. Another Kerr interior solution, arXiv, 2017. arxiv.org/pdf/1705.00584.pdf [ Links ]
V,S, Manko; I,D, Novikov. Generalizations of the Kerr and Kerr-Newman metrics possessing an arbitrary set of mass-multipole moments, Classical and Quantum Gravity 9(1992), no. 11, 2477-2487. Doi: 10.1088/0264- 9381/9/11/013 [ Links ]
P, Montero-Camacho; F, Frutos-Alfaro; C, Gutiérrez-Chaves. Slowly rotating curzon-chazy metric, Revista de Matemática: Teoría y Aplicaciones 22(2015), no. 2, 265-274. Doi: 10.15517/rmta.v22i2.20833 [ Links ]
E,T, Newman; E, Couch; K, Chinnapared; A, Exton; A, Prakash; R, Torrence. Metric of a rotating, charged mass, Journal of Mathematical Physics 6(1965), no. 6, 918-919. Doi: 10.1063/1.1704351 [ Links ]
E, Newman; R, Penrose. An approach to gravitational radiation by a method of spin coefficients, Journal of Mathematical Physics 3(1962), no. 3, 566-578. Doi: 10.1063/1.1724257 [ Links ]
G, Nordström. On the energy of the gravitation field in Einstein’s theory, Koninklijke Nederlandsche Akademie van Wetenschappen Proceedings 20(1918), no. 2, 1238-1245. [ Links ]
A,Z,Petrov.Einstein Spaces, Pergamon, Oxford, 1969. [ Links ]
H, Quevedo. Exterior and interior metrics with quadrupole moment, General Relativity and Gravitation 43(2011), no. 4, 1141-1152. Doi: 10.1007/s10714-010-0940-5 [ Links ]
H, Quevedo. Multipole moments in general relativity-static and stationary vacuum solutions, Fortschritte der Physik/Progress of Physics 38(1990), no. 10, 733-840. Doi: 10.1002/prop.2190381002 [ Links ]
H, Quevedo; B, Mashhoon. Generalization of Kerr spacetime,Physical Review D 43(1991), no. 12, 3902-3906. Doi: 10.1103/PhysRevD.43.3902 [ Links ]
M, A,RamadanFluid sources of the Kerr metric, Il Nuovo Cimento B 119(2004), no. 2, 123-129. Doi: 10.1393/ncb/i2003-10088-1 [ Links ]
A,P, Ravi; N, Banerjee. An exact interior Kerr solution, New Astronomy 64(2018), 31-33. Doi: 10.1016/j.newast.2018.04.003 [ Links ]
H, Reissner. Über die eigengravitation des elektrischen feldes nach der Einsteinschen theorie, Annalen der Physik 355(1916), no. 9, 106-120. Doi: 10.1002/andp.19163550905 [ Links ]
T, P,Sotiriou.T.A. Apostolatos, Corrections and comments on the multipole moments of axisymmetric electrovacuum spacetimes, Classical and Quantum Gravity 21(2004), no. 24. Doi: 10.1088/0264- 9381/21/24/003 [ Links ]
K,S,Thome.Multipole expansions of gravitational radiation, Reviews on Modern Physics 52(1980), no. 2, 299-340. Doi: 10.1103/RevModPhys.52.299 [ Links ]
S, Viaggiu. Interior Kerr solutions with the Newman-Janis algorithm starting with physically reasonable space-times, International Journal of Modern Physics D 15(2006), no. 9, 1441-1453. Doi: 10.1142/S0218271806009169 [ Links ]
J, Zhang; Z, Zhao. Hawking radiation of charged particles via tunneling from the Reissner-Nordström black hole, Journal of High Energy Physics 2005(2005), no. 10, 055. http://www.iopscience.iop.org/1126-6708/2005/10/055 [ Links ]
Received: August 06, 2020; Revised: November 17, 2020; Accepted: October 30, 2020
This is an open-access article distributed under the terms of the Creative Commons Attribution License
