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Revista de Matemática Teoría y Aplicaciones

Print version ISSN 1409-2433

Rev. Mat vol.22 n.2 San José Jul./Dec. 2015



Slowly rotating curzon-chazy metric

Métrica de curzon-chazy con rotación lenta

Paulo Montero-Camacho 1  

Francisco Frutos-Alfaro 2  

Carlos Gutiérrez-Chaves 3  

Iván Cordero-García 4  

1School of Physics, University of Costa Rica, San José, Costa Rica. E-Mail:

2 School of Physics, University of Costa Rica, San José, Costa Rica. E-Mail:

3 School of Physics, University of Costa Rica, San José, Costa Rica. E-Mail:

4 School of Physics, University of Costa Rica, San José, Costa Rica. E-Mail:


A new rotation version of the Curzon-Chazy metric is found. This new metric was obtained by means of a perturbation method, in order to include slow rotation. The solution is then proved to fulfill the Einstein's equations using a REDUCE program. Furthermore, the applications of this new solution are discussed.

Keywords: general relativity; solutions of Einstein's equations; approximation procedures; weak fields


Se encontró una nueva versión rotante de la métrica de Curzon-Chazy. Esta nueva métrica fue obtenida por medio de un método perturbativo para incluir rotación lenta. Se prueba que la métrica obtenida es solución a las ecuaciones de Einstein por medio de un programa en REDUCE. Finalmente, se discuten las aplicaciones de esta nueva solución.

Palabras clave: relatividad general; soluciones de las ecuaciones de Einstein; procedimientos de aproximación; campos débiles

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Abdelqader, M.; Lake, K. (2012) "Visualizing Spacetime Curvature via Gradient Flows II: An Example of the Construction of a Newtonian analogue", Physical Review 86, 124037 (ArXiv:1207.5496v2 [gr-qc]). [ Links ]

Arianrhod, R; Fletcher, S; McIntosh, C. (1991) "Principal null directions of the Curzon metric", Classical and Quantum Gravity 8(8): 1519-1528. [ Links ]

Belinski, V; Verdaguer, E. (2004) Gravitational Solitons. Cambridge University Press, United Kingdom. [ Links ]

Carmeli, M. (2001) Classical Fields. World Scientific Publishing, Singapore. [ Links ]

Chandrasekhar, S. (2000) The Mathematical Theory of Black Holes. Oxford, United Kingdom. [ Links ]

Chazy, J. (1924) "Sur le champ de gravitation de deux masses fixes dans la théorie de la relativité", Bulletin de la Société Mathématique de France 52: 17-38. [ Links ]

Curzon, H. (1924) "Cylindrical solutions of einstein's gravitation equations", Proceedings of the London Mathematical Society 23: 477-480. [ Links ]

Ernst, F. J. (1968) "New formulation of the axially symmetric gravitational field problem", Physical Review 167: 1175-1177. [ Links ]

de-Felice, F. (1990) "Potential surfaces for time-like geodesics in the Curzon metric", General Relativity and Gravitation 23(2): 136-149. [ Links ]

Gautreau, R; Anderson, J. (1967) "Directional singularities in Weyl gravitational fields", Physics Letters A 25(4): 291-292. [ Links ]

Griffiths, J; Podolský, J. (2009) Exact Space-Times in Einstein's General Relativity. Cambridge University Press, United Kingdom. [ Links ]

Halilsoy, M. (1992) "New metrics for spinning spheroids in general relativity", Journal of Mathematical Physics 33: 4225-4230. [ Links ]

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

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

Hernández-Pastora, J; Manko, V; Martín, J. (1993) "Some asymptotically flat generalizations of the Curzon metric", Journal of Mathematical Physics34: 4760-4774. [ Links ]

Kerr, R. (1963) "Gravitational field of a spinning mass as an example of algebraically special metrics", Physical Review Letters 11: 237-238. [ Links ]

Lewis, T. (1932) "Some special solutions of the equations of axially symmetric gravitational fields", Proceedings of the Royal Society (A): 176-192. [ Links ]

Stachel, J. (1968) "Structure of the Curzon metric", Physics Letters A27(1): 60-61. [ Links ]

Synge, J. (1960) Relativity: The General Theory. North Holland Publishing, Amsterdam. [ Links ]

Wanas, M; Awadalla, N; El Hanafy, W. (2012) "Strong field of binary systems and its effects on pulsar arrival times", ArXiv:1002.3399v5 [gr-qc]. [ Links ]

1Mathematics Subject Classification: 83C05, 83C20, 83C25.

Received: February 25, 2014; Revised: March 13, 2015; Accepted: May 08, 2015

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