<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>1409-2433</journal-id>
<journal-title><![CDATA[Revista de Matemática Teoría y Aplicaciones]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. Mat]]></abbrev-journal-title>
<issn>1409-2433</issn>
<publisher>
<publisher-name><![CDATA[Centro de Investigaciones en Matemática Pura y Aplicada (CIMPA) y Escuela de Matemática, San José, Costa Rica.]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1409-24332017000200239</article-id>
<article-id pub-id-type="doi">10.15517/rmta.v24i2.29856</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[On the post-linear quadrupole-quadrupole metric]]></article-title>
<article-title xml:lang="es"><![CDATA[Sobre la métrica post-lineal cuadrupolo-cuadrupolo]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Frutos-Alfaro]]></surname>
<given-names><![CDATA[Francisco]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Soffel]]></surname>
<given-names><![CDATA[Michael]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,University of Costa Rica  ]]></institution>
<addr-line><![CDATA[ San José]]></addr-line>
<country>CR</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Technical University Dresden  ]]></institution>
<addr-line><![CDATA[ Dresden]]></addr-line>
<country>DE</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2017</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2017</year>
</pub-date>
<volume>24</volume>
<numero>2</numero>
<fpage>239</fpage>
<lpage>255</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_arttext&amp;pid=S1409-24332017000200239&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_abstract&amp;pid=S1409-24332017000200239&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_pdf&amp;pid=S1409-24332017000200239&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[AbstractThe 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.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[ResumenLa 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.]]></p></abstract>
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<kwd lng="en"><![CDATA[approximation procedures]]></kwd>
<kwd lng="en"><![CDATA[weak fields]]></kwd>
<kwd lng="es"><![CDATA[relatividad general]]></kwd>
<kwd lng="es"><![CDATA[soluciones de las ecuaciones de Einstein]]></kwd>
<kwd lng="es"><![CDATA[procedimientos de aproximación]]></kwd>
<kwd lng="es"><![CDATA[campos débiles]]></kwd>
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