Square of General Relativity
Abstract
We consider dilatonaxion gravity interacting with $p\;\, U(1)$ vectors ($p=6$ corresponding to $N=4$ supergravity) in fourdimensional spacetime admitting a nonnull Killing vector field. It is argued that this theory exibits features of a ``square'' of vacuum General Relativity. In the threedimensional formulation it is equivalent to a gravity coupled $\sigma$model with the $(4+2p)$dimensional target space $SO(2,2+p)/(SO(2)\times SO(2+p))$. Kähler coordinates are introduced on the target manifold generalising Ernst potentials of General Relativity. The corresponding Kähler potential is found to be equal to the logarithm of the product of the fourdimensional metric component $g_{00}$ in the Einstein frame and the dilaton factor, independently on presence of vector fields. The Kähler potential is invariant under exchange of the Ernst potential and the complex axidilaton field, while it undergoes holomorphic/antiholomorphic transformations under general target space isometries. The ``square'' property is also manifest in the twodimensional reduction of the theory as a matrix generalization of the KramerNeugebauer map.
 Publication:

arXiv eprints
 Pub Date:
 August 1996
 arXiv:
 arXiv:grqc/9608021
 Bibcode:
 1996gr.qc.....8021G
 Keywords:

 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory
 EPrint:
 A talk at the First Australasian Conference on General Relativity and Gravitation, Adelaide, February 1217, 1996, to be published in the Proceedings