Generating Cosmological Solutions from Known Solutions

TL;DR

This paper explores three methods for generating new cosmological models from known solutions, including horizon-based techniques, variable interchange, and modern solution-generating methods, highlighting their applications and examples.

Contribution

It introduces and compares three distinct methods for constructing new cosmological solutions, emphasizing the broader potential of solution-generating techniques in cosmology.

Findings

Identification of horizon-based solution generation methods

Demonstration of variable interchange to create cosmologies

Application of modern solution techniques to cosmological models

Abstract

We consider three methods by which one can generate new cosmological models. Two of these are based on the Lorentzian structure of spacetime. In a Lorentzian manifold there can exist horizons that separate regions of spacetime that can be interpreted as cosmological models from others that have the character of ``black holes.'' A number of well known solutions of this type can be used to generate both known cosmological models and others that do not seem to have been recognized. Another method based on the Lorentzian character of spacetime is to simply interchange some space variable with time and try to restructure the metric to make a viable cosmology. A more broad-ranging method is the use of modern solution-generating techniques to construct new models. This method has been widely used to generate black hole solutions, but seems not to have been so widely used in cosmology. We will discuss examples of all three methods.