Abstract <p>Within the five-dimensional ADD model of space-time with compactification radius <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11972_2025_8799_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(R\)</EquationSource> <!--BPhysMGU2570071Grats-m1--> </InlineEquation>, we consider the classical gravitational bremsstrahlung arising from the collision of two ultrarelativistic charges. The collision is governed by the impact parameter <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11972_2025_8799_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\(b\)</EquationSource> <!--BPhysMGU2570071Grats-m2--> </InlineEquation> and the Lorentz factor <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11972_2025_8799_Article_IEq3.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\gamma\)</EquationSource> <!--BPhysMGU2570071Grats-m3--> </InlineEquation>. Using the perturbation theory, the total energy, radiated as a gravitational wave, is calculated in the leading order in <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11972_2025_8799_Article_IEq3.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\gamma\)</EquationSource> <!--BPhysMGU2570071Grats-m4--> </InlineEquation>, as well as the spectral-angular and polarization characteristics. The radiation is characterized by concentration within a cone of opening angle of order <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11972_2025_8799_Article_IEq5.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="29" /> </InlineMediaObject> <EquationSource Format="TEX">\(1/\gamma\)</EquationSource> <!--BPhysMGU2570071Grats-m5--> </InlineEquation>, with the dominant contribution coming from frequencies of order <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11972_2025_8799_Article_IEq6.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="37" /> </InlineMediaObject> <EquationSource Format="TEX">\(\gamma^{2}/b\)</EquationSource> <!--BPhysMGU2570071Grats-m6--> </InlineEquation>. The average number of Kaluza–Klein emission modes is estimated to be of the order of <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11972_2025_8799_Article_IEq7.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="44" /> </InlineMediaObject> <EquationSource Format="TEX">\(\gamma R/b\)</EquationSource> <!--BPhysMGU2570071Grats-m7--> </InlineEquation>.</p>

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Gravitational Bremsstrahlung in Collisions of Ultrarelativistic Charges in the Five-Dimensional ADD Model

  • Yu. V. Grats,
  • P. A. Spirin

摘要

Abstract

Within the five-dimensional ADD model of space-time with compactification radius \(R\) , we consider the classical gravitational bremsstrahlung arising from the collision of two ultrarelativistic charges. The collision is governed by the impact parameter \(b\) and the Lorentz factor \(\gamma\) . Using the perturbation theory, the total energy, radiated as a gravitational wave, is calculated in the leading order in \(\gamma\) , as well as the spectral-angular and polarization characteristics. The radiation is characterized by concentration within a cone of opening angle of order \(1/\gamma\) , with the dominant contribution coming from frequencies of order \(\gamma^{2}/b\) . The average number of Kaluza–Klein emission modes is estimated to be of the order of \(\gamma R/b\) .