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Carroll geodesics
Luca Ciambelli1, Daniel Grumiller1,2
1Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo, ON N2L 2Y5 Canada.
The European Physical Journal. C, Particles and Fields
|September 18, 2024
Summary
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.
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.
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