{"abstracts":[{"sha1":"f1ba318dda2fd4db6f66034417f6bdb790ea7ba2","content":"It is well known that the geometrical framework of Riemannian geometry that\nunderlies general relativity and its torsionful extension to Riemann-Cartan\ngeometry can be obtained from a procedure known as gauging the Poincare\nalgebra. Recently it has been shown that gauging the centrally extended Galilei\nalgebra, known as the Bargmann algebra, leads to a geometrical framework that\nwhen made dynamical gives rise to Horava-Lifshitz gravity. Here we consider the\ncase where we contract the Poincare algebra by sending the speed of light to\nzero leading to the Carroll algebra. We show how this algebra can be gauged and\nwe construct the most general affine connection leading to the geometry of\nso-called Carrollian space-times. Carrollian space-times appear for example as\nthe geometry on null hypersurfaces in a Lorentzian space-time of one dimension\nhigher. We also construct theories of ultra-relativistic (Carrollian) gravity\nin 2+1 dimensions with dynamical exponent z<1 including cases that have\nanisotropic Weyl invariance for z=0.","mimetype":"text/plain","lang":"en"}],"refs":[],"contribs":[{"index":0,"raw_name":"Jelle Hartong","role":"author"}],"license_slug":"ARXIV-1.0","language":"en","version":"v1","ext_ids":{"arxiv":"1505.05011v1"},"release_year":2015,"release_date":"2015-05-19","release_stage":"submitted","release_type":"article","work_id":"ceyta4sza5dypccalv54esuomm","title":"Gauging the Carroll Algebra and Ultra-Relativistic Gravity","state":"active","ident":"kcae7yt5ffhrpjs62jfmmmthgu","revision":"d82b7d44-94e2-4bfe-965c-ac1f80337d32","extra":{"arxiv":{"base_id":"1505.05011","categories":["hep-th","gr-qc"],"comments":"27 pages"}}}