<?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>0370-3908</journal-id>
<journal-title><![CDATA[Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. acad. colomb. cienc. exact. fis. nat.]]></abbrev-journal-title>
<issn>0370-3908</issn>
<publisher>
<publisher-name><![CDATA[Academia Colombiana de Ciencias Exactas, Físicas y Naturales]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0370-39082021000100030</article-id>
<article-id pub-id-type="doi">10.18257/raccefyn.1276</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Soluciones exactas de agujeros negros en la teoría generalizada de Proca]]></article-title>
<article-title xml:lang="en"><![CDATA[Exact black hole solutions in the generalized Proca theory]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Cubides Pérez]]></surname>
<given-names><![CDATA[Sergio Manuel]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Rodríguez García]]></surname>
<given-names><![CDATA[Yeinzon]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
<xref ref-type="aff" rid="Aaf"/>
<xref ref-type="aff" rid="A a"/>
<xref ref-type="aff" rid="A3"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Industrial de Santander  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad Antonio Nariño  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Salam International Centre for Theoretical Physics  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>03</month>
<year>2021</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>03</month>
<year>2021</year>
</pub-date>
<volume>45</volume>
<numero>174</numero>
<fpage>30</fpage>
<lpage>51</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0370-39082021000100030&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0370-39082021000100030&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0370-39082021000100030&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen Con el fin de restringir la teoría generalizada de Proca y de determinar su compatibilidad con las futuras observaciones en el ámbito astrofísico, se estudiaron soluciones de agujeros negros en el marco de esta teoría. Para ello, en primer lugar, se determinaron las ecuaciones de campo gravitacional y de campo vectorial correspondientes a la acción generalizada de Proca para, posteriormente, obtener sus versiones adaptadas a agujeros negros estáticos y esféricamente simétricos. Posteriormente se encontraron soluciones de las ecuaciones de campo para diferentes tipos de acoplamientos dentro de esta teoría las cuales, debido a las condiciones establecidas para las funciones métricas, difieren de las soluciones de Reissner-Nordström y de Schwarzschild tan sólo en las funciones que describen al campo vectorial dependiendo del acomplamiento estudiado. A juzgar únicamente por este resultado, la teoría de la Relatividad General luce más atractiva que la teoría generalizada de Proca.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract In order to constrain the generalized Proca theory and determine its compatibility with the future astrophysical observations, we have studied black holes solutions in the framework of this theory. To this end, in the first place, we have obtained the gravitational field and vector field equations from the generalized Proca action to subsequently obtain its adapted versions to static and spherically symmetric black holes. Later, exact solutions were found for different couplings in this theory. Due to established conditions for the metric functions, these solutions differ from the Schwarzschild and Reissner-Nordström solutions only in the functions that describe the vector field, depending on the studied coupling. Judging only from this result, General Relativity looks more attractive than the generalized Proca theory.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Agujeros negros]]></kwd>
<kwd lng="es"><![CDATA[gravedad modificada]]></kwd>
<kwd lng="es"><![CDATA[teorías vector-tensor]]></kwd>
<kwd lng="en"><![CDATA[Black holes]]></kwd>
<kwd lng="en"><![CDATA[modified gravity]]></kwd>
<kwd lng="en"><![CDATA[vector-tensor theories]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Abbott]]></surname>
<given-names><![CDATA[B. P.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Gravitational waves and gamma-rays from a binary neutron star merger: GW170817 and GRB 170817A]]></article-title>
<source><![CDATA[Astrophys. J]]></source>
<year>2017</year>
<month>a</month>
<volume>848</volume>
<page-range>L13</page-range></nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Abbott]]></surname>
<given-names><![CDATA[B. P.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[GW170817: Observation of gravitational waves from a binary neutron star inspiral]]></article-title>
<source><![CDATA[Phys. Rev. Lett]]></source>
<year>2017</year>
<month>b</month>
<volume>119</volume>
<page-range>161101</page-range></nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Abbott]]></surname>
<given-names><![CDATA[B. P.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Multi-messenger Observations of a Binary Neutron Star Merger]]></article-title>
<source><![CDATA[Astrophys. J]]></source>
<year>2017</year>
<month>c</month>
<volume>848</volume>
<page-range>L12</page-range></nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Abbott]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[GW190412: Observation of a binary-black-hole coalescence with asymmetric masses]]></article-title>
<source><![CDATA[Phys. Rev. D]]></source>
<year>2020</year>
<volume>102</volume>
<page-range>043015</page-range></nlm-citation>
</ref>
<ref id="B5">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Aghanim]]></surname>
<given-names><![CDATA[N.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Planck 2018 results. VI. Cosmological parameters]]></article-title>
<source><![CDATA[Astron. Astrophys]]></source>
<year>2020</year>
<volume>641</volume>
<page-range>A6</page-range></nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Allys]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Generalized Proca action for an Abelian vector field]]></article-title>
<source><![CDATA[JCAP]]></source>
<year>2016</year>
<month>a</month>
<volume>1602</volume>
<page-range>004</page-range></nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Allys]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Generalized SU(2) Proca Theory]]></article-title>
<source><![CDATA[Phys. Rev. D]]></source>
<year>2016</year>
<month>b</month>
<volume>94</volume>
<page-range>084041</page-range></nlm-citation>
</ref>
<ref id="B8">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Allys]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On the 4D generalized Proca action for an Abelian vector field]]></article-title>
<source><![CDATA[JCAP]]></source>
<year>2016</year>
<month>c</month>
<volume>1609</volume>
<page-range>026</page-range></nlm-citation>
</ref>
<ref id="B9">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Baker]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Strong constraints on cosmological gravity from GW170817 and GRB 170817A]]></article-title>
<source><![CDATA[Phys. Rev. Lett]]></source>
<year>2017</year>
<volume>119</volume>
<page-range>251301</page-range></nlm-citation>
</ref>
<ref id="B10">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Beltrán Jiménez]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Heisenberg]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Derivative self-interactions for a massive vector field]]></article-title>
<source><![CDATA[Phys. Lett B]]></source>
<year>2016</year>
<volume>757</volume>
<page-range>405</page-range></nlm-citation>
</ref>
<ref id="B11">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Beltrán Jiménez]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[López Maroto]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Cosmology with moving dark energy and the CMB quadrupole]]></article-title>
<source><![CDATA[Phys. Rev. D]]></source>
<year>2007</year>
<volume>76</volume>
<page-range>023003</page-range></nlm-citation>
</ref>
<ref id="B12">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Beltrán Jiménez]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Heisenberg]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Generalized multi-Proca fields]]></article-title>
<source><![CDATA[Phys. Lett. B]]></source>
<year>2017</year>
<volume>770</volume>
<page-range>16</page-range></nlm-citation>
</ref>
<ref id="B13">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ben Achour]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Degenerate higher order scalar-tensor theories beyond Horndeski and disformal transformations]]></article-title>
<source><![CDATA[Phys. Rev. D]]></source>
<year>2016</year>
<volume>93</volume>
<page-range>124005</page-range></nlm-citation>
</ref>
<ref id="B14">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bertone]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[Hooper]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[History of dark matter]]></article-title>
<source><![CDATA[Rev. Mod. Phys]]></source>
<year>2018</year>
<volume>90</volume>
<page-range>045002</page-range></nlm-citation>
</ref>
<ref id="B15">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Cai]]></surname>
<given-names><![CDATA[R. G.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Constraining the anisotropic expansion of the universe]]></article-title>
<source><![CDATA[Phys. Rev. D]]></source>
<year>2013</year>
<volume>87</volume>
<page-range>123522</page-range></nlm-citation>
</ref>
<ref id="B16">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Campanelli]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Ellipsoidal universe can solve the cosmic microwave background quadrupole problem]]></article-title>
<source><![CDATA[Phys. Rev. Lett]]></source>
<year>2006</year>
<volume>97</volume>
<page-range>131302</page-range></nlm-citation>
</ref>
<ref id="B17">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Carter]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Axisymmetric black hole has only two degrees of freedom]]></article-title>
<source><![CDATA[Phys. Rev. Lett]]></source>
<year>1971</year>
<volume>26</volume>
<page-range>331</page-range></nlm-citation>
</ref>
<ref id="B18">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Creminelli]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Vernizzi]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Dark energy after GW170817 and GRB170817A]]></article-title>
<source><![CDATA[Phys. Rev. Lett]]></source>
<year>2017</year>
<volume>119</volume>
<page-range>251302</page-range></nlm-citation>
</ref>
<ref id="B19">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Crisostomi]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Extended scalar-tensor theories of gravity]]></article-title>
<source><![CDATA[JCAP]]></source>
<year>2016</year>
<volume>1604</volume>
<page-range>044</page-range></nlm-citation>
</ref>
<ref id="B20">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Crisostomi]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Higher derivative field theories: degeneracy conditions and classes]]></article-title>
<source><![CDATA[JHEP]]></source>
<year>2017</year>
<volume>1706</volume>
<page-range>124</page-range></nlm-citation>
</ref>
<ref id="B21">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Deffayet]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Covariant Galileon]]></article-title>
<source><![CDATA[Phys. Rev. D]]></source>
<year>2009</year>
<month>a</month>
<volume>79</volume>
<page-range>084003</page-range></nlm-citation>
</ref>
<ref id="B22">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Deffayet]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Generalized Galileons: All scalar models whose curved background extensions mantain second-order field equations and stress tensors]]></article-title>
<source><![CDATA[Phys. Rev. D]]></source>
<year>2009</year>
<month>b</month>
<volume>80</volume>
<page-range>064015</page-range></nlm-citation>
</ref>
<ref id="B23">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Deffayet]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[From k-essence to generalized Galileons]]></article-title>
<source><![CDATA[Phys. Rev. D]]></source>
<year>2011</year>
<volume>84</volume>
<page-range>064039</page-range></nlm-citation>
</ref>
<ref id="B24">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Deffayet]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Steer]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A formal introduction to Horndeski and Galileon theories and their generalizations]]></article-title>
<source><![CDATA[Class. Quantum Grav]]></source>
<year>2013</year>
<volume>30</volume>
<page-range>214006</page-range></nlm-citation>
</ref>
<ref id="B25">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[de Rham]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Massive Gravity]]></article-title>
<source><![CDATA[Living Rev. Relativ]]></source>
<year>2014</year>
<volume>17</volume>
<numero>7</numero>
<issue>7</issue>
</nlm-citation>
</ref>
<ref id="B26">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[de Rham]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Resummation of Massive Gravity]]></article-title>
<source><![CDATA[Phys. Rev. Lett]]></source>
<year>2011</year>
<volume>106</volume>
<page-range>231101</page-range></nlm-citation>
</ref>
<ref id="B27">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[de Rham]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Gabadadze]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Generalization of the Fierz-Pauli action]]></article-title>
<source><![CDATA[Phys. Rev. D]]></source>
<year>2010</year>
<volume>82</volume>
<page-range>044020</page-range></nlm-citation>
</ref>
<ref id="B28">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Dong]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Quasinormal modes of black holes in scalar-tensor theories with nonminimal derivative couplings]]></article-title>
<source><![CDATA[Phys. Rev. D]]></source>
<year>2017</year>
<volume>96</volume>
<page-range>064048</page-range></nlm-citation>
</ref>
<ref id="B29">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Errasti]]></surname>
<given-names><![CDATA[V.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Complete theory of Maxwell and Proca fields]]></article-title>
<source><![CDATA[Phys. Rev. D]]></source>
<year>2020</year>
<month>a</month>
<volume>101</volume>
<page-range>045008</page-range></nlm-citation>
</ref>
<ref id="B30">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Errasti]]></surname>
<given-names><![CDATA[V.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Maxwell-Proca theory: Definition and construction]]></article-title>
<source><![CDATA[Phys. Rev. D]]></source>
<year>2020</year>
<month>b</month>
<volume>101</volume>
<page-range>045009</page-range></nlm-citation>
</ref>
<ref id="B31">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ezquiaga]]></surname>
<given-names><![CDATA[J. M.]]></given-names>
</name>
<name>
<surname><![CDATA[Zumalacárregui]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Dark energy after GW170817: Dead ends and the road ahead]]></article-title>
<source><![CDATA[Phys. Rev. Lett]]></source>
<year>2017</year>
<volume>119</volume>
<page-range>251304</page-range></nlm-citation>
</ref>
<ref id="B32">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Gallego Cadavid]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Rodríguez]]></surname>
<given-names><![CDATA[Y.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A systematic procedure to build the beyond generalized Proca field theory]]></article-title>
<source><![CDATA[Phys. Lett. B]]></source>
<year>2019</year>
<volume>798</volume>
<page-range>134958</page-range></nlm-citation>
</ref>
<ref id="B33">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ganguly]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Black hole stability under odd-parity perturbations in Horndeski gravity]]></article-title>
<source><![CDATA[Class. Quantum Grav]]></source>
<year>2018</year>
<volume>35</volume>
<page-range>145008</page-range></nlm-citation>
</ref>
<ref id="B34">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Gleyzes]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[New Class of Consistent Scalar-Tensor Theories]]></article-title>
<source><![CDATA[Phys. Rev. Lett]]></source>
<year>2015</year>
<volume>114</volume>
<page-range>211101</page-range></nlm-citation>
</ref>
<ref id="B35">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hassan]]></surname>
<given-names><![CDATA[S. F.]]></given-names>
</name>
<name>
<surname><![CDATA[Rosen]]></surname>
<given-names><![CDATA[R. A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Bimetric gravity from ghost-free massive gravity]]></article-title>
<source><![CDATA[JHEP]]></source>
<year>2012</year>
<volume>1202</volume>
<page-range>126</page-range></nlm-citation>
</ref>
<ref id="B36">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Heisenberg]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Generalization of the Proca action]]></article-title>
<source><![CDATA[JCAP]]></source>
<year>2014</year>
<volume>1405</volume>
<page-range>015</page-range></nlm-citation>
</ref>
<ref id="B37">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Heisenberg]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Beyond generalized Proca theories]]></article-title>
<source><![CDATA[Phys. Lett. B]]></source>
<year>2016</year>
<volume>760</volume>
<page-range>617</page-range></nlm-citation>
</ref>
<ref id="B38">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Heisenberg]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Black holes in vector-tensor theories]]></article-title>
<source><![CDATA[JCAP]]></source>
<year>2017</year>
<volume>1708</volume>
<page-range>024</page-range></nlm-citation>
</ref>
<ref id="B39">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Heisenberg]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Odd-parity stability of hairy black holes in U(1) gauge-invariant scalar-vector-tensor theories]]></article-title>
<source><![CDATA[Phys. Rev. D]]></source>
<year>2018</year>
<volume>97</volume>
<page-range>124043</page-range></nlm-citation>
</ref>
<ref id="B40">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hinterbichler]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Theorical aspects of massive gravity]]></article-title>
<source><![CDATA[Rev. Mod. Phys]]></source>
<year>2012</year>
<volume>84</volume>
<page-range>671</page-range></nlm-citation>
</ref>
<ref id="B41">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hinterbichler]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
<name>
<surname><![CDATA[Rosen]]></surname>
<given-names><![CDATA[R. A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Interacting spin-2 fields]]></article-title>
<source><![CDATA[JHEP]]></source>
<year>2012</year>
<volume>1207</volume>
<page-range>047</page-range></nlm-citation>
</ref>
<ref id="B42">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Horndeski]]></surname>
<given-names><![CDATA[H. W.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Second-order-scalar-tensor field equations in a four-dimensional space]]></article-title>
<source><![CDATA[Int. J. Theor. Phys]]></source>
<year>1974</year>
<volume>10</volume>
<page-range>363-84</page-range></nlm-citation>
</ref>
<ref id="B43">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kase]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Black hole perturbations in vector-tensor theories: the odd-mode]]></article-title>
<source><![CDATA[JCAP]]></source>
<year>2018</year>
<volume>1802</volume>
<page-range>048</page-range></nlm-citation>
</ref>
<ref id="B44">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kase]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Tsujikawa]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Dark energy in Horndeski theories after GW170817: A review]]></article-title>
<source><![CDATA[Int. J. Mod. Phys. D]]></source>
<year>2019</year>
<volume>28</volume>
<page-range>1942005</page-range></nlm-citation>
</ref>
<ref id="B45">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kimura]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Extended vector-tensor theories]]></article-title>
<source><![CDATA[JCAP]]></source>
<year>2017</year>
<volume>1701</volume>
<page-range>002</page-range></nlm-citation>
</ref>
<ref id="B46">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kobayashi]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Black hole perturbation in the most general scalar-tensor theory with second-order field equations: The odd-parity sector]]></article-title>
<source><![CDATA[Phys. Rev. D]]></source>
<year>2012</year>
<volume>85</volume>
<page-range>084025</page-range></nlm-citation>
</ref>
<ref id="B47">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kobayashi]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Black hole perturbation in the most general scalar-tensor theory with second-order field equations. II. The even-parity sector]]></article-title>
<source><![CDATA[Phys. Rev. D]]></source>
<year>2014</year>
<volume>89</volume>
<page-range>084042</page-range></nlm-citation>
</ref>
<ref id="B48">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Langlois]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Noui]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Degenerate higher derivative theories beyond Horndeski: evading the ostrogradski instability]]></article-title>
<source><![CDATA[JCAP]]></source>
<year>2016</year>
<volume>1602</volume>
<page-range>034</page-range></nlm-citation>
</ref>
<ref id="B49">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Martin-Garcia]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<source><![CDATA[xact: Efficient tensor computer algebra for the wolfram language]]></source>
<year>2019</year>
<publisher-name><![CDATA[Xact.es]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B50">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Nicolis]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Galileon as a local modification of gravity]]></article-title>
<source><![CDATA[Phys. Rev. D]]></source>
<year>2009</year>
<volume>79</volume>
<page-range>064036</page-range></nlm-citation>
</ref>
<ref id="B51">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ostrogradski]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Memoires sur les equations differentielles relatives au problem des isoperimetres]]></article-title>
<source><![CDATA[Mem. Ac. St. Petersbourg VI]]></source>
<year>1850</year>
<volume>4</volume>
<page-range>385</page-range></nlm-citation>
</ref>
<ref id="B52">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Perlmutter]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Measurements of Q and A from 42 High-Redshift Supernovae]]></article-title>
<source><![CDATA[Astrophys. J]]></source>
<year>1999</year>
<volume>517</volume>
<page-range>565</page-range></nlm-citation>
</ref>
<ref id="B53">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Riess]]></surname>
<given-names><![CDATA[A. G.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Observational evidence from supernovae for an accelerating universe and a cosmological constant]]></article-title>
<source><![CDATA[Astronom. J]]></source>
<year>1998</year>
<volume>116</volume>
<page-range>1009</page-range></nlm-citation>
</ref>
<ref id="B54">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Robinson]]></surname>
<given-names><![CDATA[D. C.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Uniqueness of the Kerr black hole]]></article-title>
<source><![CDATA[Phys. Rev. Lett]]></source>
<year>1975</year>
<volume>34</volume>
<page-range>905</page-range></nlm-citation>
</ref>
<ref id="B55">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Rodrigues]]></surname>
<given-names><![CDATA[D. C.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Anisotropic cosmological constant and the CMB quadrupole anomaly]]></article-title>
<source><![CDATA[Phys. Rev. D]]></source>
<year>2008</year>
<volume>77</volume>
<page-range>023534</page-range></nlm-citation>
</ref>
<ref id="B56">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Rodríguez]]></surname>
<given-names><![CDATA[Y.]]></given-names>
</name>
<name>
<surname><![CDATA[Navarro]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Scalar and vector Galileons]]></article-title>
<source><![CDATA[J. Phys.: Conf. Ser]]></source>
<year>2017</year>
<volume>831</volume>
<page-range>012004</page-range></nlm-citation>
</ref>
<ref id="B57">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Sakstein]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Jain]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Implications of the neutron star merger GW170817 for cosmological scalar-tensor theories]]></article-title>
<source><![CDATA[Phys. Rev. Lett]]></source>
<year>2017</year>
<volume>119</volume>
<page-range>251303</page-range></nlm-citation>
</ref>
<ref id="B58">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Tasinato]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Cosmic acceleration from Abelian symmetry breaking]]></article-title>
<source><![CDATA[JHEP]]></source>
<year>2014</year>
<month>a</month>
<volume>1404</volume>
<page-range>067</page-range></nlm-citation>
</ref>
<ref id="B59">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Tasinato]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A small cosmological constant from Abelian symmetry breaking]]></article-title>
<source><![CDATA[Class. Quantum Grav]]></source>
<year>2014</year>
<month>b</month>
<volume>31</volume>
<page-range>225004</page-range></nlm-citation>
</ref>
<ref id="B60">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Tattersall]]></surname>
<given-names><![CDATA[O. J.]]></given-names>
</name>
<name>
<surname><![CDATA[Ferreira]]></surname>
<given-names><![CDATA[P. G.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Quasinormal modes of black holes in Horndeski gravity]]></article-title>
<source><![CDATA[Phys. Rev. D]]></source>
<year>2018</year>
<volume>97</volume>
<page-range>104047</page-range></nlm-citation>
</ref>
<ref id="B61">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Wang]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The GW170817/GRB 170817A/AT 2017gfo Association: Some Implications for Physics and Astrophysics]]></article-title>
<source><![CDATA[Astrophys. J.]]></source>
<year>2017</year>
<volume>851</volume>
<page-range>L18</page-range></nlm-citation>
</ref>
<ref id="B62">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Woodard]]></surname>
<given-names><![CDATA[R. P.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Avoiding dark energy with 1/R modifications of gravity]]></article-title>
<source><![CDATA[Lec. Notes Phys.]]></source>
<year>2007</year>
<volume>720</volume>
<page-range>403</page-range></nlm-citation>
</ref>
<ref id="B63">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Woodard]]></surname>
<given-names><![CDATA[R. P.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Ostrogradsky's theorem on Hamiltonian instability]]></article-title>
<source><![CDATA[Scholarpedia]]></source>
<year>2015</year>
<volume>10</volume>
<page-range>32243</page-range></nlm-citation>
</ref>
</ref-list>
</back>
</article>
