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Torsional Carroll Gravity.

Patrick Concha1,2, Nelson Merino3,4, Lucrezia Ravera2,5,6

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This study introduces Carrollian Mielke-Baekler gravity, a new model for ultrarelativistic gravity. It reveals nonvanishing temporal torsion and curvature in three-dimensional Carrollian gravity, unifying existing theories.

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Area of Science:

  • Theoretical physics
  • Gravitational physics
  • Mathematical physics

Background:

  • The ultrarelativistic (Carrollian) regime offers a novel framework for studying holography and non-Lorentzian symmetries.
  • Understanding the geometric limits of general relativity is crucial for advancing gravitational theories.

Purpose of the Study:

  • To establish the presence of nonvanishing torsion in three-dimensional Carrollian gravity.
  • To construct the Carrollian Mielke-Baekler (C-MB) gravity theory.
  • To present the most general three-dimensional Carrollian gravity model with temporal and spatial curvature.

Main Methods:

  • Constructing the Carrollian Mielke-Baekler (C-MB) gravity theory.
  • Utilizing the Chern-Simons formulation.
  • Deriving the C-MB theory as the ultrarelativistic limit of the relativistic Mielke-Baekler model.

Main Results:

  • Established nonvanishing temporal torsion and curvature in three-dimensional Carrollian gravity.
  • The C-MB theory incorporates spatial curvature, providing a comprehensive Carrollian gravity model.
  • Demonstrated that temporal torsion influences null generators and boundary dynamics.

Conclusions:

  • The C-MB gravity framework unifies several known ultrarelativistic gravity theories.
  • This model offers a generalized approach to three-dimensional Carrollian gravity.
  • The findings advance the understanding of non-Lorentzian gravity and its holographic implications.