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Carroll geodesics.

Luca Ciambelli1, Daniel Grumiller1,2

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We derived the Carrollian geodesic action, revealing coupled electric and magnetic terms. Carrollian geodesics exhibit unique dynamics, with unstable circular orbits and half the light-bending deflection angle compared to general relativity.

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Area of Science:

  • Theoretical Physics
  • Gravitational Physics
  • Effective Field Theory

Background:

  • Geodesic motion is fundamental in understanding spacetime dynamics.
  • Carrollian spacetimes offer a unique theoretical framework distinct from standard relativistic models.

Purpose of the Study:

  • To derive the Carrollian analog of the geodesic action.
  • To explore the dynamics of Carrollian geodesics, particularly on a Carroll-Schwarzschild background.

Main Methods:

  • Application of effective field theory methods.
  • Derivation of equations of motion from the Carrollian geodesic action.

Main Results:

  • The Carrollian geodesic action includes coupled electric and magnetic contributions.
  • Carrollian geodesics display rich dynamics, including an effective potential with energy-dependent Newton term.
  • A single, unstable circular orbit exists at the Carroll extremal surface.
  • Deflection angle for large impact parameters is half the general relativistic value.
  • Geodesics exhibit reflection for small impact parameters, acting as a perfect mirror.

Conclusions:

  • Carrollian gravity presents distinct geodesic dynamics compared to standard general relativity.
  • The Carroll-Schwarzschild black hole exhibits unique reflective properties for infalling particles.