  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.
