Carroll limit of four-dimensional gravity theories in the first order formalism
arXiv:2107.10129 · doi:10.1088/1361-6382/ac345f
Abstract
We explore the ultra-relativistic limit of a class of four dimensional gravity theories, known as Lovelock-Cartan gravities, in the first order formalism. First, we review the well known limit of the Einstein-Hilbert action. A very useful scale symmetry involving the vierbeins and the boost connection is presented. Moreover, we explore the field equations in order to find formal solutions. Some remarkable results are obtained: Riemann and Weitzenböck like manifolds are discussed; Birkhoff's theorem is verified for the torsionless case; an explicit solution with non-trivial geometry is discussed; A quite general solution in the presence of matter is obtained. Latter, we consider the ultra-relativistic limit of the more general Lovelock-Cartan gravity. The previously scale symmetry is also discussed. The field equations are studied in vacuum and in the presence of matter. In comparison with the Einstein-Hilbert case, a few relevant results are found: Birkhoff's theorem is also verified for the torsionless case; A quite general solution in the presence of matter is obtained. This solution generalizes the previous case; Riemann and Weitzenböck like manifolds are derived in the same lines of the Einstein-Hilbert case.
arXiv comment22 pages; 1 figure
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