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Mathematics Subject Classification: 83C05, 83C25, 85-02.
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Revista de Matemática Teoría y Aplicaciones
versão impressa ISSN 1409-2433
Rev. Mat vol.24 no.2 San José Jul./Dez. 2017
http://dx.doi.org/10.15517/rmta.v24i2.29856
Artículo
On the post-linear quadrupole-quadrupole metric
Sobre la métrica post-lineal cuadrupolo-cuadrupolo
1School of Physics and Space Research Center, University of Costa Rica, San José, Costa Rica. E-Mail: frutos@fisica.ucr.ac.cr
2Technical University Dresden and Lohrmann Observatory, Dresden, Germany. E-Mail: Michael.Soffel@mailbox.tu-dresden.de
The Hartle-Thorne metric defines a reliable spacetime for most astrophysical purposes, for instance simulations of slowly rotating stars. Solving the Einstein field equations, we added terms of second order in the quadrupole moment to its post-linear version in order to compare it with solutions found by Blanchet in the multi-polar post-Minkowskian framework. We first derived the extended Hartle-Thorne metric in harmonic coordinates and then showed agreement with the corresponding post-linear metric from Blanchet.
We also found a coordinate transformation from the post-linear ErezRosen metric to our extended Hartle-Thorne spacetime. It is well known that the Hartle-Thorne solution can be smoothly matched with an interior perfect fluid solution with appropriate physical properties. A comparison among these solutions provides a validation of them. It is clear that in order to represent realistic solutions of self-gravitating (axially symmetric) matter distributions of perfect fluid, the quadrupole moment has to be included as a physical parameter.
Keywords: general relativity; solutions of Einstein’s equations; approximation procedures; weak fields
La métrica de Hartle-Thorne define un espacio-tiempo confiable para la mayoría de propósitos astrofísicos, por ejemplo simulaciones de estrellas girando lentamente. Añadimos términos de segundo orden en el momento cuadripolar a su versión post-lineal al resolver las ecuaciones de campo de Einstein. La solución encontrada es comparada con la encontrada por Blanchet en el marco post-Minkowskiano. Primero derivamos la métrica de Hartle-Thorne en coordenadas armónicas y luego mostramos la concordancia con la correspondiente métrica post-lineal de Blanchet.
También encontramos una transformación de coordenadas de la métrica de Erez-Rosen post-lineal al espacio-tiempo de Hartle-Thorne obtenido. Es bien sabido que la solución de Hartle-Thorne puede estar suavemente acoplada con una solución de fluido interior perfecto con propiedades físicas apropiadas. Una comparación entre estas soluciones proporciona una validación de las mismas. Está claro que para representar soluciones realistas de distribuciones de materia auto-gravitantes (axialmente simétricas) de fluido perfecto, el momento cuadripolar tiene que ser incluido como un parámetro físico.
Palabras clave: relatividad general; soluciones de las ecuaciones de Einstein; procedimientos de aproximación; campos débiles
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Received: May 25, 2016; Revised: April 17, 2017; Accepted: April 28, 2017
This is an open-access article distributed under the terms of the Creative Commons Attribution License
