Towards a unified Lagrangian formalism for Cosmology and Black Holes

TL;DR

This paper develops a unified Lagrangian framework linking higher-dimensional cosmology, black holes, and string theory, revealing that key solutions like FRW and Schwarzschild emerge naturally from this formalism.

Contribution

It introduces a novel Lagrangian approach that unifies cosmological and black hole solutions within a two-dimensional metric derived from Einstein-Hilbert action.

Findings

FRW cosmology derived from the Lagrangian formalism

Schwarzschild black hole solution obtained from the same framework

Establishment of a connection between higher-dimensional gravity and string actions

Abstract

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.