Sigma-model approaches to exact solutions in higher-dimensional gravity and supergravity

Abstract

Classical gravitating field theories reduced to three dimensions admit manifest gauge invariances and hidden symmetries, which together make up the invariance group G of the theory. If this group is large enough, the target space is a symmetric space G/H. New solutions may be generated by the action of invariance transformations on a seed solution. Another application is the construction of multicenter solutions from null geodesics of the target space. After a general introduction on this sigma-model approach, I will discuss the case of five-dimensional gravity, with invariace group SL(3,R), and minimal five-dimensional supergravity, with invariance group G_{2(2)}. I will also describe recent attempts at the generation of new charged rotating black rings.

28 pages, 1 figure, talk presented at the WE Heraeus Seminar on Models of Gravity in Higher Dimenions: From Theory to Experimental Search, Bremen, 25-29.8.2008

References in corpus (10)

• General Non-Extremal Rotating Black Holes in Minimal Five-Dimensional Gauged Supergravity
• Black ring with two angular momenta
• Higher-dimensional Origin of D=3 Coset Symmetries
• Integrable Systems in Stringy Gravity
• $G_2$ generating technique for minimal D=5 supergravity and black rings
• A rotating black lens solution in five dimensions
• From Schwarzschild to Kerr: Generating spinning Einstein-maxwell fields from static fields
• The symmetries of five-dimensional minimal supergravity reduced to three dimensions
• Non-asymptotically flat black holes/branes
• Generating rotating fields in general relativity