Geometric Flow of Bubbles

TL;DR

This paper derives and analyzes geometric flow equations for metric-scalar systems, applying them to bubble solutions to understand their flow behavior, with implications for string theory and geometric analysis.

Contribution

It introduces a new class of geometric flow equations derived from string frame actions and applies them to scalar and metric bubble solutions.

Findings

Flow equations are successfully derived from string frame actions.

Application to bubble solutions reveals their flow behavior.

Provides insights into geometric evolution in scalar-metric systems.

Abstract

In this work we derive a class of geometric flow equations for metric-scalar systems. Thereafter, we construct them from some general string frame action by performing volume-preserving fields variations and writing down the associated gradient flow equations. Then, we consider some specific realisations of the above procedure, applying the flow equations to non-trivial scalar bubble and metric bubble solutions, studying the subsequent flow behaviour.