<?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>S1409-24332015000200255</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[A visualization of null geodesics for the bonnor massive dipole]]></article-title>
<article-title xml:lang="es"><![CDATA[Visualización de geodésicas nulas para el dipolo masivo de bonnor]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Oliva-Mercado]]></surname>
<given-names><![CDATA[G. Andree]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Bonatti-González]]></surname>
<given-names><![CDATA[Javier]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Cordero-García]]></surname>
<given-names><![CDATA[Iván]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<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-group>
<aff id="Af1">
<institution><![CDATA[,Universidad de Costa Rica Escuela de Física ]]></institution>
<addr-line><![CDATA[ San José]]></addr-line>
<country>CR</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad de Costa Rica Escuela de Física ]]></institution>
<addr-line><![CDATA[ San José]]></addr-line>
<country>CR</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Universidad de Costa Rica Escuela de Física ]]></institution>
<addr-line><![CDATA[ San José]]></addr-line>
<country>CR</country>
</aff>
<aff id="Af4">
<institution><![CDATA[,Universidad de Costa Rica Centro de Investigaciones Espaciales (CINESPA) ]]></institution>
<addr-line><![CDATA[ San José]]></addr-line>
<country>CR</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2015</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2015</year>
</pub-date>
<volume>22</volume>
<numero>2</numero>
<fpage>255</fpage>
<lpage>264</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_arttext&amp;pid=S1409-24332015000200255&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_abstract&amp;pid=S1409-24332015000200255&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_pdf&amp;pid=S1409-24332015000200255&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[AbstractIn this work we simulate null geodesics for the Bonnor massive dipole metric by implementing a symbolic-numerical algorithm in Sage and Python. This program is also capable of visualizing in 3D, in principle, the geodesics for any given metric. Geodesics are launched from a common point, collectively forming a cone of light beams, simulating a solid-angle section of a point source in front of a massive object with a magnetic field. Parallel light beams also were considered, and their bending due to the curvature of the space-time was simulated.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[ResumenEn este trabajo se simulan geodésicas nulas para la métrica de dipolo masivo de Bonnor, implementando un algoritmo simbólico-numérico en Sage y Python. Este programa es capaz, en principio, de visualizar en 3D las geodésicas de cualquier métrica. Estas geodésicas inician en un punto común, formando colectivamente un cono de rayos de luz, simulando una sección de ángulo sólido de una fuente puntual frente a un objeto masivo con campo magnético. Se consideran también rayos de luz paralelos, y se simuló su cambio de trayectoria debida a la curvatura del espacio-tiempo.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[general relativity]]></kwd>
<kwd lng="en"><![CDATA[geodesics]]></kwd>
<kwd lng="en"><![CDATA[differential geometry]]></kwd>
<kwd lng="en"><![CDATA[free software]]></kwd>
<kwd lng="es"><![CDATA[relatividad general]]></kwd>
<kwd lng="es"><![CDATA[geodésicas]]></kwd>
<kwd lng="es"><![CDATA[geometría diferencial]]></kwd>
<kwd lng="es"><![CDATA[software libre]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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