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<p>We conduct studies on Levin’s taxonomy of periodic orbits for neutral test particles around a Reissner-Nordström naked singularity. It was known that naked singularities could harbor two distinct regions of time-like bound orbits and thus we expect periodic orbits to appear in both regions. It is possible for a pair of periodic orbits from both regions to possess the exact same angular momentum <i>L</i> and energy <i>E</i> values. We chart the sets of periodic orbits in (<i>L</i>,&#xa0;<i>E</i>)-parameter space and highlight the general distribution pattern of these sets for three possible scenarios. Regions within (<i>L</i>,&#xa0;<i>E</i>)-space can be partitioned into multiple domains <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10714_2025_3368_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mathcal {D}}_k\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">D</mi> <mi>k</mi> </msub> </math></EquationSource> </InlineEquation> based on the roots configuration of the quartic polynomial <i>P</i>(<i>u</i>) where <i>u</i> is the inverse radial coordinate. Consequently, each domain and interestingly enough, portions of certain periodic orbits sets that lie in different <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10714_2025_3368_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mathcal {D}}_k\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">D</mi> <mi>k</mi> </msub> </math></EquationSource> </InlineEquation> require different analytical solutions to plot the resulting orbit. Furthermore, we uncover physical properties of some hypothetical circular orbits residing in the inner region from analysing the (<i>L</i>,&#xa0;<i>E</i>)-space.</p>

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Periodic orbits of neutral test particles in Reissner–Nordström naked singularities

  • 期刊论文

  • 发表日期：

    2025年2月4日

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  • Zoe C. S. Chan,
  • Yen-Kheng Lim

摘要

We conduct studies on Levin’s taxonomy of periodic orbits for neutral test particles around a Reissner-Nordström naked singularity. It was known that naked singularities could harbor two distinct regions of time-like bound orbits and thus we expect periodic orbits to appear in both regions. It is possible for a pair of periodic orbits from both regions to possess the exact same angular momentum L and energy E values. We chart the sets of periodic orbits in (L, E)-parameter space and highlight the general distribution pattern of these sets for three possible scenarios. Regions within (L, E)-space can be partitioned into multiple domains \({\mathcal {D}}_k\) D k based on the roots configuration of the quartic polynomial P(u) where u is the inverse radial coordinate. Consequently, each domain and interestingly enough, portions of certain periodic orbits sets that lie in different \({\mathcal {D}}_k\) D k require different analytical solutions to plot the resulting orbit. Furthermore, we uncover physical properties of some hypothetical circular orbits residing in the inner region from analysing the (L, E)-space.