Magnetic Carrollian gravity from the Carroll algebra

Abstract

We explicitly establish the equivalence between the magnetic Carrollian limit of Einstein gravity defined through the Hamiltonian formalism and the Carrollian theory of gravity defined through a gauging of the Carroll algebra along the lines of standard Poincaré (or (A)dS) gaugings.

Non-Lorentzian theories with and without constraints

“…Some of the models we construct in this way are new to the best of our knowledge and we give some preliminary analysis of their physical significance. It would be very interesting to extend our analysis to gravity, possibly producing new non-Lorentzian gravitational models beyond the ones already known [8,10,14,25,27,36,37].…”

“…This is motivated by their relevance to many physical situations in e.g. applications to condensed matter physics [4,5], hydrodynamics [6][7][8] and gravitational problems [9][10][11][12][13][14]. They have also featured prominently in non-relativistic variants of holography [15][16][17].…”

“…The second instance is the Carrollian limit where the speed of light is formally small compared to the characteristic velocities of the system [10,13,14,[23][24][25][26][27]. The associated Carroll algebra can also be obtained by a contraction of the Poincaré algebra [28,29] and is given in (2.10).…”

Constructing Carrollian Field Theories from Null Reduction

“…One is by gauging the Carrollian algebra [58][59][60], and the other is by using the contraction of Lorentz theory [28]. A comparison between the magnetic theory from Carrollian contraction and the construction from gauge procedure were made in [61], while the electric sector is missing in the gauging description. The Bargmann reduction may shed light on this subtle issue, as it could in principle lead to both the electric and magnetic sectors at the same time.…”

Electric/magnetic Newton-Hooke and Carroll Jackiw-Teitelboim gravity

“…Also, it has been recently shown that the Hamiltonian formulation of general relativity admits at least two Carroll limits [21]. The so-called magnetic case is equivalent to the Carroll theory of gravity, defined through a gauging of the Carroll algebra [22].…”