Towards a unified Lagrangian formalism for Cosmology and Black Holes
  Using a Lagrangian formalism we establish a relationship between the (n + D + d) dimensional cosmology, black-holes and the Polyakov action for strings. Specifically, we identify these physical scenarios as part of a 2-dimensional metric, which arises from a Lagrangian function with constraints, derived from the Einstein-Hilbert action. In particular, we show that the Friedmann-Robertson-Walker cosmological model and the Schwarzschild solution are both consequence of this Lagrangian. 
G. Avila and J. A. Nieto
physics.gen-ph