The Universality of vacuum Einstein equations with cosmological constant

摘要: It is shown that for a wide class of analytic Lagrangians, which depend only on the scalar curvature metric and connection, application so called `Palatini formalism', i.e. treating connection as independent variables, leads to `universal' equations. If dimension n spacetime greater than two these universal equations are vacuum Einstein with cosmological constant generic Lagrangian suitably replaced by other at degenerate points. We show degeneracy takes place in particular conformally invariant Lagrangians we prove their solutions equivalent Einstein's For two-dimensional spacetimes find instead equation always curvature; this case Weyl containing Levi-Civita an additional vector field ensuing from conformal invariance. As example, investigate detail some polynomial discuss