Positive-energy theorem forR+R2gravity

Abstract

We prove that asymptotically flat extrema of the action $S=\ensuremath{\int}[R+(\frac{1}{2{\ensuremath{\beta}}^{2}}){R}^{2}]$ have non-negative energy, provided there exists a spacelike hypersurface on which $Rg\ensuremath{-}{\ensuremath{\beta}}^{2}$. Flat space is shown to be the unique topologically Minkowskian stationary point of the energy. This result leads to a heuristic functional variational argument for positivity that does not involve restrictions on $R$. We also prove that flat space is semiclassically stable. Possible extensions of the theorems and relevance to quantum gravity are briefly discussed.