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Revista de Matemática Teoría y Aplicaciones

Print version ISSN 1409-2433

Rev. Mat vol.28 n.2 San José Jul./Dec. 2021 


Approximate Kerr-Newman-like metric with quadrupole

Métrica aproximada tipo Kerr-Newman con cuadrupolo

Francisco Frutos-Alfaro1 

Pedro Gómez-Ovares2 

Paulo Montero-Camacho3 

1Universidad de Costa Rica, Escuela de Física, Centro de Investigaciones Espaciales (CINESPA), San José, Costa Rica;

2Universidad de Costa Rica, Escuela de Física, Centro de Investigaciones Espaciales (CINESPA), San José, Costa Rica;

3Tsinghua University, Department of Astronomy, Beijing, China;


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.

Mathematics Subject Classification: 83C05, 83C25, 85-02.

Ver contenido completo en PDF.


Thanks to the referees for their constructive and valuable observations that allowed an improvement of the manuscript.


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Received: August 06, 2020; Revised: November 17, 2020; Accepted: October 30, 2020

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