<?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>0035-001X</journal-id>
<journal-title><![CDATA[Revista mexicana de física]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. mex. fis.]]></abbrev-journal-title>
<issn>0035-001X</issn>
<publisher>
<publisher-name><![CDATA[Sociedad Mexicana de Física]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0035-001X2022000400002</article-id>
<article-id pub-id-type="doi">10.31349/revmexfis.68.040701</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Cosmological-static metric correspondence and Kruskal type solutions from symmetry transformations]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Nieto]]></surname>
<given-names><![CDATA[J. A.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[León]]></surname>
<given-names><![CDATA[E. A.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[García-Quintero]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Autonóma de Sinaloa Facultad de Ciencias Físico-Matemáticas ]]></institution>
<addr-line><![CDATA[Culiacán Sinaloa]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,University of Texas Department of Physics ]]></institution>
<addr-line><![CDATA[Dallas TX]]></addr-line>
<country>USA</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>08</month>
<year>2022</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>08</month>
<year>2022</year>
</pub-date>
<volume>68</volume>
<numero>4</numero>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S0035-001X2022000400002&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S0035-001X2022000400002&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S0035-001X2022000400002&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract We develop a formalism which provides a new view for the transformation of spherically symmetric metrics, regarding cosmological and Kruskal type metrics. Our analysis begins with some general relevant dynamically metrics in cosmology, and prove that they all can be transformed to a unique static form. We extend the formalism to obtain generalized Kruskal type coordinates in cosmology and black hole theory. This extended formalism provides a novel mechanism to obtain suitable coordinate charts associated with spherically symmetric metrics. In particular, we obtain explicitly new Kruskal type coordinates for extremal Reissner-Nordström and Schwarzschild-de-Sitter metrics, as well for an extension of the de-Sitter metric.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Cosmology]]></kwd>
<kwd lng="en"><![CDATA[black holes]]></kwd>
<kwd lng="en"><![CDATA[symmetries]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<label>1</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Misner]]></surname>
<given-names><![CDATA[C. W.]]></given-names>
</name>
<name>
<surname><![CDATA[Thorne]]></surname>
<given-names><![CDATA[K.S.]]></given-names>
</name>
<name>
<surname><![CDATA[Wheeler]]></surname>
<given-names><![CDATA[J.A.]]></given-names>
</name>
</person-group>
<source><![CDATA[Gravitation]]></source>
<year>1970</year>
<page-range>616-7</page-range><publisher-loc><![CDATA[San Francisco CA ]]></publisher-loc>
<publisher-name><![CDATA[W. H. Freeman and Company]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B2">
<label>2</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Carroll]]></surname>
<given-names><![CDATA[S. M.]]></given-names>
</name>
</person-group>
<source><![CDATA[Spacetime and geometry: An introduction to general relativity]]></source>
<year>2004</year>
<page-range>329-36</page-range><publisher-loc><![CDATA[San Francisco CA ]]></publisher-loc>
<publisher-name><![CDATA[Addison-Wesley]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[León]]></surname>
<given-names><![CDATA[E. A.]]></given-names>
</name>
<name>
<surname><![CDATA[Nieto]]></surname>
<given-names><![CDATA[J. A.]]></given-names>
</name>
<name>
<surname><![CDATA[Nunez-Lopez]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Lipovka]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Higher Dimensional Cosmology: Relations among the radii of two homogeneous spaces]]></article-title>
<source><![CDATA[Mod. Phys. Lett. A]]></source>
<year>2011</year>
<volume>26</volume>
<page-range>805</page-range></nlm-citation>
</ref>
<ref id="B4">
<label>4</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Zink]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
<name>
<surname><![CDATA[Schnetter]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Tiglio]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Multipatch methods in general relativistic astrophysics: Hydrodynamical flows on fixed backgrounds]]></article-title>
<source><![CDATA[Phys. Rev. D]]></source>
<year>2008</year>
<volume>77</volume>
<page-range>103015</page-range></nlm-citation>
</ref>
<ref id="B5">
<label>5</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Giblin]]></surname>
<given-names><![CDATA[J. T.]]></given-names>
</name>
<name>
<surname><![CDATA[Marolf]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Garvey]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Spacetime Embedding Diagrams for Spherically Symmetric Black Holes]]></article-title>
<source><![CDATA[Gen. Rel. Grav.]]></source>
<year>2004</year>
<volume>36</volume>
<page-range>83</page-range></nlm-citation>
</ref>
<ref id="B6">
<label>6</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Melia]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The apparent (gravitational) horizon in cosmology]]></article-title>
<source><![CDATA[Am. J. Phys.]]></source>
<year>2018</year>
<volume>86</volume>
<page-range>585</page-range></nlm-citation>
</ref>
<ref id="B7">
<label>7</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Tolman]]></surname>
<given-names><![CDATA[R. C.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On the Astronomical Implications of the de Sitter Line Element for the Universe]]></article-title>
<source><![CDATA[Astrophys. J.]]></source>
<year>1929</year>
<volume>69</volume>
<page-range>245</page-range></nlm-citation>
</ref>
<ref id="B8">
<label>8</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Lanczos]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Ein vereinfachendes Koordinatensystem für Einsteinschen Gravitationsgleichungen]]></article-title>
<source><![CDATA[Phys. Zeit.]]></source>
<year>1922</year>
<volume>23</volume>
<page-range>539</page-range></nlm-citation>
</ref>
<ref id="B9">
<label>9</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Agacy]]></surname>
<given-names><![CDATA[R. L.]]></given-names>
</name>
<name>
<surname><![CDATA[McCrea]]></surname>
<given-names><![CDATA[W. H.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A Transformation of the De Sitter Metric and the law of Creation of Matter]]></article-title>
<source><![CDATA[MNRAS]]></source>
<year>1962</year>
<volume>123</volume>
<page-range>383</page-range></nlm-citation>
</ref>
<ref id="B10">
<label>10</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Burg]]></surname>
<given-names><![CDATA[M. G. J. van der]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Transformations Leaving the De Sitter Line-Element Invariant]]></article-title>
<source><![CDATA[MNRAS]]></source>
<year>1966</year>
<volume>131</volume>
<page-range>499</page-range></nlm-citation>
</ref>
<ref id="B11">
<label>11</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Florides]]></surname>
<given-names><![CDATA[P. S.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The Robertson-Walker metrics expressible in static form]]></article-title>
<source><![CDATA[Gen. Rel. Grav.]]></source>
<year>1980</year>
<volume>12</volume>
<page-range>563</page-range></nlm-citation>
</ref>
<ref id="B12">
<label>12</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Mitra]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[When can an &#8220;Expanding Universe&#8221; look &#8220;Static&#8221; and vice versa: A comprehensive study]]></article-title>
<source><![CDATA[Int. J. Mod. Phys D]]></source>
<year>2015</year>
<volume>24</volume>
<page-range>1550032</page-range></nlm-citation>
</ref>
<ref id="B13">
<label>13</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Melia]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Cosmological redshift in Friedmann-Robertson-Walker metrics with constant space-time curvature]]></article-title>
<source><![CDATA[MNRAS]]></source>
<year>2012</year>
<volume>422</volume>
<page-range>1418</page-range></nlm-citation>
</ref>
<ref id="B14">
<label>14</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kruskal]]></surname>
<given-names><![CDATA[M. D.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Maximal Extension of Schwarzschild Metric]]></article-title>
<source><![CDATA[Phys. Rev.]]></source>
<year>1960</year>
<volume>119</volume>
<page-range>1743</page-range></nlm-citation>
</ref>
<ref id="B15">
<label>15</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Szekeres]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On the Singularities of a Riemannian Manifold]]></article-title>
<source><![CDATA[Publ. Math. Debrecen]]></source>
<year>1960</year>
<volume>7</volume>
<page-range>285</page-range></nlm-citation>
</ref>
<ref id="B16">
<label>16</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Aviles-Niebla]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Nieto-Marin]]></surname>
<given-names><![CDATA[P. A.]]></given-names>
</name>
<name>
<surname><![CDATA[Nieto]]></surname>
<given-names><![CDATA[J. A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Towards exterior/interior correspondence of black-holes]]></article-title>
<source><![CDATA[Int. J. Geom. Meth. Mod. Phys.]]></source>
<year>2020</year>
<volume>17</volume>
<page-range>2050180</page-range></nlm-citation>
</ref>
<ref id="B17">
<label>17</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Graves]]></surname>
<given-names><![CDATA[J. C.]]></given-names>
</name>
<name>
<surname><![CDATA[Brill]]></surname>
<given-names><![CDATA[D. R.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Oscillatory Character of Reissner-Nordström Metric for an Ideal Charged Wormhole]]></article-title>
<source><![CDATA[Phys. Rev.]]></source>
<year>1960</year>
<volume>120</volume>
<page-range>1507</page-range></nlm-citation>
</ref>
<ref id="B18">
<label>18</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Guo]]></surname>
<given-names><![CDATA[J.-Q.]]></given-names>
</name>
<name>
<surname><![CDATA[Joshi]]></surname>
<given-names><![CDATA[P. S.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Interior dynamics of neutral and charged black holes]]></article-title>
<source><![CDATA[Phys. Rev. D]]></source>
<year>2015</year>
<volume>92</volume>
<page-range>064013</page-range></nlm-citation>
</ref>
<ref id="B19">
<label>19</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Nieto]]></surname>
<given-names><![CDATA[J. A.]]></given-names>
</name>
<name>
<surname><![CDATA[Leon]]></surname>
<given-names><![CDATA[E. A.]]></given-names>
</name>
<name>
<surname><![CDATA[Villanueva]]></surname>
<given-names><![CDATA[V. M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Higher-Dimensional Charged Black Holes as Constrained Systems]]></article-title>
<source><![CDATA[Int. J. Mod. Phys. D]]></source>
<year>2013</year>
<volume>22</volume>
<page-range>1350047</page-range></nlm-citation>
</ref>
<ref id="B20">
<label>20</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Cruz]]></surname>
<given-names><![CDATA[N.]]></given-names>
</name>
<name>
<surname><![CDATA[Olivares]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Villanueva]]></surname>
<given-names><![CDATA[J. R.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The golden ratio in Schwarzschild-Kottler black holes]]></article-title>
<source><![CDATA[Eur. Phys. J. C]]></source>
<year>2017</year>
<volume>77</volume>
<page-range>123</page-range></nlm-citation>
</ref>
<ref id="B21">
<label>21</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Gibbons]]></surname>
<given-names><![CDATA[G. W.]]></given-names>
</name>
<name>
<surname><![CDATA[Hawking]]></surname>
<given-names><![CDATA[S. W.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Cosmological event horizons, thermodynamics, and particle creation]]></article-title>
<source><![CDATA[Phys. Rev. D]]></source>
<year>1977</year>
<volume>15</volume>
<page-range>2738</page-range></nlm-citation>
</ref>
<ref id="B22">
<label>22</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Beck]]></surname>
<given-names><![CDATA[J. F.]]></given-names>
</name>
<name>
<surname><![CDATA[Inomata]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Kruskal-like representation of the de Sitter metric]]></article-title>
<source><![CDATA[J. Math. Phys.]]></source>
<year>1984</year>
<volume>25</volume>
<page-range>3039</page-range></nlm-citation>
</ref>
<ref id="B23">
<label>23</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Rindler]]></surname>
<given-names><![CDATA[W.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Analogies between Kruskal space and de Sitter space]]></article-title>
<source><![CDATA[Found. Phys.]]></source>
<year>1985</year>
<volume>15</volume>
<page-range>545</page-range></nlm-citation>
</ref>
<ref id="B24">
<label>24</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Akcay]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Matzner]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The Kerr-de Sitter universe]]></article-title>
<source><![CDATA[Class. Quant. Grav.]]></source>
<year>2011</year>
<volume>28</volume>
<page-range>085012</page-range></nlm-citation>
</ref>
<ref id="B25">
<label>25</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[González-Díaz]]></surname>
<given-names><![CDATA[P. F.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Generalized de Sitter space]]></article-title>
<source><![CDATA[Phys. Rev. D]]></source>
<year>2000</year>
<volume>61</volume>
<page-range>024019</page-range></nlm-citation>
</ref>
<ref id="B26">
<label>26</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Podolsky]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The Structure of the Extreme Schwarzschild-de Sitter Space-time]]></article-title>
<source><![CDATA[Gen. Rel. Grav.]]></source>
<year>1999</year>
<volume>31</volume>
<page-range>1703</page-range></nlm-citation>
</ref>
<ref id="B27">
<label>27</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Varadarajan]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Kruskal coordinates as canonical variables for Schwarzschild black holes]]></article-title>
<source><![CDATA[Phys. Rev. D]]></source>
<year>2001</year>
<volume>63</volume>
<page-range>084007</page-range></nlm-citation>
</ref>
<ref id="B28">
<label>28</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Jacobson]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[When is gttgrr = &#8722;1?]]></article-title>
<source><![CDATA[Class. Quant. Grav.]]></source>
<year>2007</year>
<volume>24</volume>
<page-range>5717</page-range></nlm-citation>
</ref>
<ref id="B29">
<label>29</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bronnikov]]></surname>
<given-names><![CDATA[K. A.]]></given-names>
</name>
<name>
<surname><![CDATA[Elizalde]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Odintsov]]></surname>
<given-names><![CDATA[S. D.]]></given-names>
</name>
<name>
<surname><![CDATA[Zaslavskii]]></surname>
<given-names><![CDATA[O. B.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Horizons versus singularities in spherically symmetric space-times]]></article-title>
<source><![CDATA[Phys. Rev. D]]></source>
<year>2008</year>
<volume>78</volume>
<page-range>064049</page-range></nlm-citation>
</ref>
<ref id="B30">
<label>30</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Lake]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Some notes on the Kruskal-Szekeres completion]]></article-title>
<source><![CDATA[Class. Quant. Grav.]]></source>
<year>2010</year>
<volume>27</volume>
<page-range>097001</page-range></nlm-citation>
</ref>
<ref id="B31">
<label>31</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Canfora]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
<name>
<surname><![CDATA[Giacomini]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Troncoso]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Black holes, parallelizable horizons, and half-BPS states for the Einstein-Gauss-Bonnet theory in five dimensions]]></article-title>
<source><![CDATA[Phys. Rev. D]]></source>
<year>2008</year>
<volume>77</volume>
<page-range>024002</page-range></nlm-citation>
</ref>
<ref id="B32">
<label>32</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Nieto]]></surname>
<given-names><![CDATA[J. A.]]></given-names>
</name>
<name>
<surname><![CDATA[Alejo-Armenta]]></surname>
<given-names><![CDATA[L. N.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Hurwitz theorem and parallelizable spheres from tensor analysis]]></article-title>
<source><![CDATA[Int. J. Mod. Phys. A]]></source>
<year>2001</year>
<volume>16</volume>
<page-range>4207</page-range></nlm-citation>
</ref>
</ref-list>
</back>
</article>
