Abstract
In this work, we present the three-dimensional Maxwell Carroll gravity by considering the ultra-relativistic limit of the Maxwell Chern-Simons gravity theory defined in three spacetime dimensions. We show that an extension of the Maxwellian Carroll symmetry is necessary in order for the invariant tensor of the ultra-relativistic Maxwellian algebra to be non-degenerate. Consequently, we discuss the origin of the aforementioned algebra and theory as a flat limit. We show that the theoretical setup with cosmological constant yielding the extended Maxwellian Carroll Chern-Simons gravity in the vanishing cosmological constant limit is based on a new enlarged extended version of the Carroll symmetry. Indeed, the latter exhibits a non-degenerate invariant tensor allowing the proper construction of a Chern-Simons gravity theory which reproduces the extended Maxwellian Carroll gravity in the flat limit.
Highlights
Symmetries in Physics play a fundamental role in the analysis and understanding of theories.In this perspective, ultra-relativistic (UR) symmetries, known as Carroll symmetries, have attracted some interest over recent years
In this work we have presented novel UR symmetries being Maxwellian generalizations and enlargements of the Carroll symmetry
In the Maxwellian case, we have shown that an extended version of the Maxwell Carroll algebra, which we have denoted as Maxwellian Extended Carroll (MEC) algebra, is required in order to avoid degeneracy
Summary
Symmetries in Physics play a fundamental role in the analysis and understanding of theories. To the NR case, an extended version of the Maxwell Carroll is required Such extension is necessary in order for the invariant tensor to be non-degenerate and allow the proper construction of a CS action. We show that the model with cosmological constant yielding the Maxwellian extended Carroll CS gravity theory in the limit of vanishing cosmological is based on an enlarged extended version of the Carroll symmetry exhibiting a non-degenerate invariant tensor and allowing the proper construction of a CS gravity theory.
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