Exact Hypersurface-Homogeneous Solutions in Cosmology and Astrophysics

TL;DR

The paper introduces a unifying framework for understanding and deriving exact hypersurface-homogeneous solutions in Einstein's equations, applicable to cosmology and astrophysics, and extends to other gravitational theories.

Contribution

It develops a Hamiltonian-based method to find and analyze hypersurface-homogeneous solutions, simplifying and unifying previous approaches and extending applicability to alternative gravity theories.

Findings

Unified framework for hypersurface-homogeneous solutions

Methods for exploiting hidden symmetries and invariant submanifolds

Extension to Brans-Dicke and higher-dimensional theories

Abstract

A framework is introduced which explains the existence and similarities of most exact solutions of the Einstein equations with a wide range of sources for the class of hypersurface-homogeneous spacetimes which admit a Hamiltonian formulation. This class includes the spatially homogeneous cosmological models and the astrophysically interesting static spherically symmetric models as well as the stationary cylindrically symmetric models. The framework involves methods for finding and exploiting hidden symmetries and invariant submanifolds of the Hamiltonian formulation of the field equations. It unifies, simplifies and extends most known work on hypersurface-homogeneous exact solutions. It is shown that the same framework is also relevant to gravitational theories with a similar structure, like Brans-Dicke or higher-dimensional theories.