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@ARTICLE{Jiang:643308,
      author       = {Jiang, Qiqi and Li, Guang-Xing and Singh, Chandra B.},
      title        = {{D}ispersion relation for the linear theory of relativistic
                      {R}ayleigh–{T}aylor instability in a magnetized medium
                      revisited},
      reportid     = {PUBDB-2026-00114, arXiv:2411.03347. DESY-24-008},
      year         = {2026},
      abstract     = {The Rayleigh–Taylor instability (RTI) arises at the
                      interface between two fluids of different densities, notably
                      when a heavier fluid lies above a lighter one in an
                      effective gravitational field. In astrophysical systems with
                      high velocities, relativistic corrections are necessary. We
                      investigate the linear theory of the relativistic
                      Rayleigh-Taylor instability (R-RTI) in a magnetized medium,
                      where fluids can move with relativistic velocities. We chose
                      an "intermediate frame" in which the fluids on each side of
                      the interface move in opposite directions with identical
                      Lorentz factors $\gamma_*$ and derive the new dispersion
                      relation of the R-RTI. This symmetry facilitates analytical
                      derivations and the study of relativistic effects on the
                      dynamics of instabilities. We find that the instability is
                      activated when the Atwood number $\mathcal{A}$ = $(\rho_1
                      h_1 - \rho_2 h_2) / (\rho_1 h_1 + \rho_2 h_2) >0$, where
                      $\rho_1$ and $\rho_2$ are densities measured in the rest of
                      the fluids. The relativistic effect is mostly contained in
                      the Lorentz transformation of the effective acceleration $g'
                      = g \gamma_*^{-2}$, which, combined with time dilation,
                      leads to a much slower growth of instability
                      ($\omega'=\gamma_*^{-1} \omega_0$), and a slightly elongated
                      length of the unstable patch, due to weaker $g$ in the
                      intermediate frame. Taking time dilation into account, when
                      viewed in the rest frame of the medium, we expect the
                      instability to grow at a much reduced rate. The analytical
                      results should guide further explorations of instability in
                      systems such as microquasars ($\mu$QSOs), Active galactic
                      nuclei (AGNs), gamma-ray bursts (GRBs), and radio pulsars
                      (PSRs), where the apparent stability of the jet can be
                      attributed to either the intrinsic stability (e.g. the
                      Atwood number) or the much prolonged duration through which
                      R-RTI can grow.},
      keywords     = {Instabilities (autogen) / Magnetohydrodynamics (autogen) /
                      Relativistic process (autogen) / Jets (autogen)},
      cin          = {$Z_THAT$},
      ddc          = {530},
      cid          = {$I:(DE-H253)Z_THAT-20210408$},
      pnm          = {613 - Matter and Radiation from the Universe (POF4-613)},
      pid          = {G:(DE-HGF)POF4-613},
      experiment   = {EXP:(DE-MLZ)NOSPEC-20140101},
      typ          = {PUB:(DE-HGF)25},
      eprint       = {2411.03347},
      howpublished = {arXiv:2411.03347},
      archivePrefix = {arXiv},
      SLACcitation = {$\%\%CITATION$ = $arXiv:2411.03347;\%\%$},
      doi          = {10.3204/PUBDB-2026-00114},
      url          = {https://bib-pubdb1.desy.de/record/643308},
}