  
  
Stat 
Members: 3661 Articles: 2'599'751 Articles rated: 2609
11 November 2024 

   

Article overview
 

The Universality of Einstein Equations  M.Ferraris
; M.Francaviglia
; I.Volovich
;  Date: 
2 Mar 1993  Subject:  grqc hepth  Abstract:  It is shown that for a wide class of analytic Lagrangians which depend only on the scalar curvature of a metric and a connection, the application of the socalled ``Palatini formalism’’, i.e., treating the metric and the connection as independent variables, leads to ``universal’’ equations. If the dimension $n$ of spacetime is greater than two these universal equations are Einstein equations for a generic Lagrangian and are suitably replaced by other universal equations at bifurcation points. We show that bifurcations take place in particular for conformally invariant Lagrangians $L=R^{n/2} sqrt g$ and prove that their solutions are conformally equivalent to solutions of Einstein equations. For 2dimensional spacetime we find instead that the universal equation is always the equation of constant scalar curvature; the connection in this case is a Weyl connection, containing the LeviCivita connection of the metric and an additional vectorfield ensuing from conformal invariance. As an example, we investigate in detail some polynomial Lagrangians and discuss their bifurcations.  Source:  arXiv, grqc/9303007  Services:  Forum  Review  PDF  Favorites 


No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.

 


