Formalism
Definition
Spacetime configurations
Properties
Spacetimes
black hole spacetimes | vanishing angular momentum | positive angular momentum |
---|---|---|
vanishing charge | Schwarzschild spacetime | Kerr spacetime |
positive charge | Reissner-Nordstrom spacetime | Kerr-Newman spacetime |
Quantum theory
What is sometimes called de Sitter gravity and anti de Sitter gravity is the analog of Einstein gravity with the local model geometry of Minkowski spacetime acted on by the Poincaré group replaced by anti de Sitter spacetime or de Sitter spacetime acted on by their isometry groups (anti de Sitter group and de Sitter group, respectively).
More in detail, in the first order formulation of gravity the field configurations of Einstein gravity (general relativity) are Cartan connections for the inclusion of the Spin group into the Poincaré group. Accordingly a field configuration of anti de Sitter (resp. de Sitter) gravity is a Cartan connection for a suitable stabilizer subgroup included into (resp. ).
Paul Townsend, Small Scale Structure of Space-Time as the Origin of the Gravitational Constant, Phys.Rev. D15 (1977) 2795 (spire)
Takeshi Fukuyama, Gauge theory of gravity, Zeitschrift für Physik C Particles and Fields 1981, Volume 10, Issue 1, pp 9-15 (publisher)
A. Achúcarro and Paul Townsend, A Chern-Simons Action for Three-Dimensional anti-De Sitter Supergravity Theories , Phys. Lett. B180 (1986) 89.
Edward Witten, (2+1)-Dimensional Gravity as an Exactly Soluble System Nucl. Phys. B311 (1988) 46. (web)
Leonardo Castellani, Riccardo D'Auria, Pietro Fré, volume 1, chapter I.4.4 of Supergravity and Superstrings - A Geometric Perspective, World Scientific (1991)
Derek Wise, MacDowell-Mansouri gravity and Cartan geometry, Class.Quant.Grav.27:155010,2010 (arXiv:gr-qc/0611154)
Theo Verwimp, Anti-de Sitter gauge theory for gravity (arXiv:1006.1614)
Wikipedia, de Sitter invariant special relativity
M. Gunaydin, Peter van Nieuwenhuizen, N.P. Warner, General Construction of the Unitary Representations of Anti-de Sitter Superalgebras and the Spectrum of the Compactification of Eleven-dimensional Supergravity, Nucl.Phys. B255 (1985) 63 (spire)
Last revised on August 3, 2018 at 16:14:16. See the history of this page for a list of all contributions to it.