Lie-algebra expansions, Chern-Simons theories and the Einstein-Hilbert lagrangian

Abstract

Starting from gravity as a Chern-Simons action for the AdS algebra in five dimensions, it is possible to deform the theory through an expansion of the Lie algebra that leads to a system consisting of the Einstein-Hilbert action plus nonminimally coupled matter. The deformed system is gauge invariant under the Poincare group enlarged by an Abelian ideal. Although the resulting action naively looks like General Relativity plus corrections due to matter sources, it is shown that the nonminimal couplings produce a radical departure from GR. Indeed, the dynamics is not continuously connected to the one obtained from Einstein-Hilbert action. In a matter-free configuration and in the torsionless sector, the field equations are too strong a restriction on the geometry as the metric must satisfy both the Einstein and pure Gauss-Bonnet equations. In particular, the five-dimensional Schwarzschild geometry fails to be a solution; however, configurations corresponding to a brane-world with positive cosmological constant on the worldsheet are admissible when one of the matter fields is switched on. These results can be extended to higher odd dimensions.

11 pages

References in corpus (4)

• Simple compactifications and Black p-branes in Gauss-Bonnet and Lovelock Theories
• The Chern-Simons One-form and Gravity on a Fuzzy Space
• Towards a Chern-Simons M theory of $OSp(1|32)\times OSp(1|32)$
• The Matrix Chern-Simons One-form as a Universal Chern-Simons Theory

Cited by in corpus (46)

• Standard General Relativity from Chern-Simons Gravity
• Generalized cosmological term from Maxwell symmetries
• Expansions of algebras and superalgebras and some applications
• Pure Lovelock gravity and Chern-Simons theory
• Eleven-Dimensional Gauge Theory for the M Algebra as an Abelian Semigroup Expansion of osp(32|1)
• Generalized Chern-Simons higher-spin gravity theories in three dimensions
• On the Maxwell supergravity and flat limit in 2+1 dimensions
• Generalizing the ${\mathfrak{bms}}_3$ and 2D-conformal algebras by expanding the Virasoro algebra
• Higher-spin Chern-Simons theories in odd dimensions
• Minimal AdS-Lorentz supergravity in three-dimensions
• New family of Maxwell like algebras
• Lovelock gravities from Born-Infeld gravity theory
• Three-dimensional Maxwellian extended Bargmann supergravity
• General properties of the expansion methods of Lie algebras
• Generalized Pure Lovelock Gravity
• Non-relativistic three-dimensional supergravity theories and semigroup expansion method
• The Universe as a topological defect
• On the supersymmetry invariance of flat supergravity with boundary
• Three-dimensional Poincaré supergravity and $\mathcal{N}$-extended supersymmetric BMS${}_3$ algebra
• Generalized Maxwellian exotic Bargmann gravity theory in three spacetime dimensions
• Semi-simple enlargement of the ${\mathfrak{bms}}_3$ algebra from a $\mathfrak{so}(2,2)\oplus \mathfrak{so}(2,1)$ Chern-Simons theory
• Three-dimensional exotic Newtonian supergravity theory with cosmological constant
• Three-dimensional Maxwellian Extended Newtonian gravity and flat limit
• Asymptotic Symmetries of Maxwell Chern-Simons Gravity with Torsion
• Sources for Chern-Simons theories
• (p,q) D=3 Poincare supergravities from Lie algebra expansions
• Resonant algebras and gravity
• Hypersymmetric extensions of Maxwell Chern-Simons gravity in (2+1) dimensions
• (Super-)Gravities of a different sort
• Topological obstructions in Lagrangian field theories, with an application to 3D Chern-Simons gauge theory
• Resonant superalgebras and $\mathcal{N}=1$ supergravity theories in three spacetime dimensions
• Resonant algebras in Chern-Simons model of topological insulators
• Brane gravity in 4D from Chern-Simons gravity theory
• Local supersymmetric extensions of the Poincare and AdS invariant gravity
• 4D spin-2 fields from 5D Chern-Simons theory
• Stellar equilibrium in Einstein-Chern-Simons gravity
• On a Java library to perform S-expansions of Lie algebras
• Supersymmetric algebra of the massive supermembrane
• A Java library to perform S-expansions of Lie algebras
• Scalar-tensor theory with EGB term from Einstein Chern-Simons gravity
• Three-dimensional non-relativistic Hietarinta supergravity
• Semigroup Expansion and M-Supergravity in Eleven Dimensions
• Einstein-Chern-Simons equations on the 3-brane world
• Resonant superalgebras for supergravity
• Three-dimensional Maxwellian Carroll gravity theory and the cosmological constant
• Maxwell Chern-Simons gravity in 3D: Thermodynamics of cosmological solutions and black holes with torsion