Test compatible metrics and 2-branes

Abstract

We propose a sufficient condition for a general spherical symmetric static metric to be compatible with classical tests of gravity. A 1-parametric class of such metrics are constructed. The Schwarzschild metric as well as the Yilmaz-Rosen metric are in this class. By computing the scalar curvature we show that the non-Schwarzschild metrics can be interpreted as close 2-branes. All the manifolds endowed the described metrics contain in a class of pseudo-Riemannian manifolds with a scalar curvature of a fixed sign.