Gauging the Carroll algebra and ultra-relativistic gravity

By J. Hartong. 2015

211 citations recorded by the source corpus.

A bstractIt is well known that the geometrical framework of Riemannian geometry that underlies general relativity and its torsionful extension to Riemann-Cartan geometry can be obtained from a procedure known as gauging the Poincaré algebra. Recently it has been shown that gauging the centrally extended Galilei algebra, known as the Bargmann algebra, leads to a geometrical framework that when made dynamical gives rise to Hořava-Lifshitz gravity. Here we consider the case where we contract the Poincaré algebra by sending the speed of light to zero leading to the Carroll algebra. We show how this algebra can be gauged and we construct the most general affine connection leading to the geometry of so-called Carrollian space-times. Carrollian space-times appear for example as the geometry on null hypersurfaces in a Lorentzian space-time of one dimension higher. We also construct theories of ultra-relativistic (Carrollian) gravity in 2+1 dimensions with dynamical exponent z < 1 including cases that have anisotropic Weyl invariance for z = 0.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/65a86d1094d750a135e42e01d91ee3e381d9e3db

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Citations in the corpus

Carroll contractions of Lorentz-invariant theories (2021, methodology): “In fact, covariant actions for Carroll gravity have been constructed in [34, 35] by gauging the Carroll algebra2.”
Carroll versus Galilei gravity (2017, background): “(3)A different version of Carroll gravity has been studied in [12].”
Carroll structures, null geometry, and conformal isometries (2019, background): “it spans the vertical subbundle Vr. The horizontal subbundle Hr is given by the set of vectors X in TCr that are orthogonal to n: X · n = 0; (38) 6Our choice of gauge ﬁxing diﬀers from other works as [6,20]. 6 but since X ∈ Hr, by deﬁnition X ·ℓ = 0. (39) Thus, writing X = Xr∂r +Xt∂t +Xi∂i, Eqs. (38”
Flat holography: aspects of the dual field theory (2016, background): “Some preliminary steps have been taken in [59, 60].”
Lifshitz holography (2015, background): “Finally, we should mention that one can also consider ultra-relativistic limits in which one sends the speed of light to zero; such limits and the corresponding geometry of Carrollian spacetimes were explored in [145].”
Carrollian physics at the black hole horizon (2019, background): “Actually, it is now understood that any null hypersurface is endowed with a Carrollian geometry1 [10,12–16] and that the associated constraint equations are ultra-relativistic conservation laws [17].”