Dimensional Reduction of Gravity and Relation between Static States, Cosmologies and Waves

TL;DR

This paper explores generalized dimensional reductions of 1+1-dimensional dilaton gravity, revealing deep connections between static states, cosmologies, and waves, including new wave solutions with finite matter fields everywhere in space-time.

Contribution

It introduces novel reduction methods applicable to integrable and non-integrable models, establishing links between different gravitational configurations and extending previous work with new solutions.

Findings

Found wave solutions depending on space and time variables.

Discovered solutions with matter fields finite everywhere.

Demonstrated the connection between static states, cosmologies, and waves.

Abstract

We introduce generalized dimensional reductions of an integrable 1+1-dimensional dilaton gravity coupled to matter down to one-dimensional static states (black holes in particular), cosmological models and waves. An unusual feature of these reductions is the fact that the wave solutions depend on two variables - space and time. They are obtained here both by reducing the moduli space (available due to complete integrability) and by a generalized separation of variables (applicable also to non integrable models and to higher dimensional theories). Among these new wave-like solutions we have found a class of solutions for which the matter fields are finite everywhere in space-time, including infinity. These considerations clearly demonstrate that a deep connection exists between static states, cosmologies and waves. We argue that it should exist in realistic higher-dimensional theories as well. Among other things we also briefly outline the relations existing betweenthe low-dimensional models that we have discussed hereand the realistic higher-dimensional ones. This paper develops further some ideas already present in our previous papers. We briefly reproduce here (without proof) their main results in a more concise form and give an important generalization.