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Magnetically Induced Rotating Rayleigh-Taylor Instability
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Ghosts without Runaway Instabilities.

Cédric Deffayet1,2, Shinji Mukohyama3,4, Alexander Vikman5

  • 1𝒢ℝϵℂ𝒪, Institut d'Astrophysique de Paris, UMR 7095, CNRS, Sorbonne Université, 98bis boulevard Arago, 75014 Paris, France.

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We show that mechanical systems with negative kinetic terms, or "ghosts," can be completely stable. This challenges the common belief that such systems are inherently unstable, even with unbounded Hamiltonians.

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Area of Science:

  • Theoretical Physics
  • Classical Mechanics
  • Cosmology

Background:

  • Systems with negative kinetic terms, often termed 'ghosts,' are relevant in modern cosmology, quantum gravity, and high energy physics.
  • These systems are typically presumed to be unstable due to their properties.

Purpose of the Study:

  • To investigate the stability of mechanical systems featuring a canonical degree of freedom interacting with a ghost degree of freedom.
  • To analytically and numerically demonstrate the stability of such systems.

Main Methods:

  • Development of a simple class of mechanical models with interacting degrees of freedom, one possessing a negative kinetic term.
  • Analytical proof of the classical motion's stability for all initial conditions.
  • Support of analytical findings through numerical computations.

Main Results:

  • The classical motion of the described mechanical system is proven to be completely stable for all initial conditions.
  • The stability holds true despite the conserved Hamiltonian being unbounded from below and above.
  • Numerical computations fully corroborate the analytical stability results.

Conclusions:

  • The common assumption of instability for systems with negative kinetic terms may be an oversimplification.
  • Mechanical systems incorporating 'ghost' degrees of freedom can exhibit stable classical motion.
  • This finding opens new perspectives for understanding systems with ghosts in physics.