Geometric Flow of Bubbles

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.

Entropy functionals and thermodynamics of relativistic geometric flows, stationary quasi-periodic Ricci solitons, and gravity

“…s-structure) of a cotangent Lorentz bundle M = T * V, dim V = 4, as in [12,13,41]. Star product R-flux deformations of fundamental geometry s-objects (27), determined by nonassociative geometric data s g ⋆ (τ ), s D ⋆ (τ ) , are performed following Convention 2 (26) with κ-linear parametric decompositions when ⋆ ǧ[0] αsβs (τ ) = ⋆ g αsβs (τ ) = g αsβs (τ ). Geometric flows on a parameter τ are described in [0]-approximation (zero power on κ) by flows of some canonical data ( s g(τ ), s D(τ )), star product flows ⋆ s (τ ), determined by s-adapted frames e is (τ ) in (19), and flows of volume elements…”

“…We omit such technical details in this work because they can be derived in abstract form following geometric principles and the Convention 2 (26). For recent applications in high energy physics, we cite [23,24,25,26,27] where the normalizing function is postulated as a dilaton field and associative and commutative versions of metric-dilaton Ricci flows are investigated. Certain geometric flow equations can be also motivated as star product R-flux deformations of a two-dimensional sigma model with beta functions and dilaton field (see equations ( 79) and (80) in [23]).…”

“…In connection to this, we note the swampland program [19,20,21] which main goal is to elaborate rigorous criteria how to distinguish the low-energy effective field theories that can be completed in the UV from those that cannot. The swampland hypothesis in quantum gravity, QG, the infinite distance conjecture and various other someway related conjectures, were revisited recently in a series of works [22,23,24,25,26,27] using (non) commutative geometric flow, exact solutions in gravity theories, and quantum field methods. Here we emphasize that to elaborate on rigorous algebraic and geometric approaches to mathematical particle physics and QG, we have to consider models of nonassociative quantum mechanics, QM, [30,31] and further developments with nonassicative and noncommutative algebras [32,33,15,34,35,36].…”

“…9 1.2 The structure, aims, and the main hypothesis of the paper This work is a natural and logical development of a series of articles on nonassociative geometry and physics [37,38,39] and a new research program on nonassociative geometric and quantum information flows and gravity [12,13,40,41]. It is related to the swampland program [19,20,21] and revised conjectures [23,24,25,26,27] following such five aims:…”

“…In fact, for the AdS spaces, the Ricci flow swampland conjecture is equivalent to the anti-de Sitter distance conjecture (ADS) [20,23,24]. Swampland conjectures were studied recently in connection to BH physics, extra dimensions and geometric flow conjectures, when the concept of Bekenstein-Hawking entropy was applied [25,26,27]. A modern approach to QG and string and M-theory involves models with nonassocitative structures for QM, QFT and MGTs.…”