Paper · Nov 8, 2022

On-Shell Flow

Davide De Biasio

hep-tharXiv:2211.04231
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Abstract

In this work, the problem of constructing geometric flow equations that preserve Einstein field equations for the spacetime metric is addressed. After having briefly discussed the main features of Ricci flow, the on-shell flow equations for a system comprised of a dynamical metric and a set of matter fields are constructed. Then, two examples in which the matter content is just a single, self-interacting scalar field are analysed in detail, imposing the geometric flow equations to be the action-induced ones. In conclusion, an explicit connection to the Swampland Distance Conjecture is proposed.

Comments: 72 pages, 18 figures

Ricci flowPhysics

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Connected papers

The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2021, plus the canon.

Connected papers This paper in the centre and the 8 papers closest to it around it, in date order clockwise from the top. The closer a paper sits to the centre, the stronger the connection. This paper Cobordism, Singularities and the Ricci Flow Conjecture (David Martín Velázquez, Davide De Biasio and Dieter Lust, 2022)4Velázquez 2022 Gradient flow of Einstein-Maxwell theory and Reissner-Nordström black holes (Davide De Biasio, Julian Freigang, Dieter Lust et al., 2022)5De Biasio 2022 A path integral formula of quantum gravity emergent from entangled local structures (Jinglong Liu, Stephon Alexander, Antonino Marciano et al., 2023)6Liu 2023 Aspects of the Classical Double Copy (Rashid Alawadhi, 2023)7Alawadhi 2023 Geometric flows and the Swampland (Davide De Biasio, 2023)1De Biasio 2023 Dark energy and dark matter configurations for wormholes and solitionic hierarchies of nonmetric Ricci flows and F(R,T,Q,Tₘ) gravity (Laurenţiu Bubuianu, Sergiu I. Vacaru, Elşen Veli Veliev et al., 2024)3Bubuianu 2024 Solutions to the Ricci Flow via Einstein Field Equations (Tommaso Morone and Roberto Tateo, 2024)2Morone 2024 Navigating string theory field space with geometric flows (Saskia Demulder, Dieter Lust and Thomas Raml, 2024)8Demulder 2024
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Geometric flows and the Swampland

    Davide De Biasio PDF

    Topics Physics · Same author Davide De Biasio · Shared terms “geometric flows”, “Swampland”, “action induced”

  2. Solutions to the Ricci Flow via Einstein Field Equations

    Tommaso Morone and Roberto Tateo PDF

    Topics Physics · Shared terms “Einstein field”, “field equations”, “preserves”

  3. Dark energy and dark matter configurations for wormholes and solitionic hierarchies of nonmetric Ricci flows and gravity

    Laurenţiu Bubuianu, Sergiu I. Vacaru, Elşen Veli Veliev et al. PDF

    Topics Physics · Shared terms “geometric flows”, “matter fields”, “field equations”

  4. Cobordism, Singularities and the Ricci Flow Conjecture

    David Martín Velázquez, Davide De Biasio and Dieter Lust PDF

    Topics Ricci flow · Same author Davide De Biasio · Shared terms “Swampland Distance”, “Distance Conjecture”

  5. Gradient flow of Einstein-Maxwell theory and Reissner-Nordström black holes

    Davide De Biasio, Julian Freigang, Dieter Lust et al. PDF

    Topics Physics · Same author Davide De Biasio · Shared terms “preserves”, “Einstein”

  6. A path integral formula of quantum gravity emergent from entangled local structures

    Jinglong Liu, Stephon Alexander, Antonino Marciano et al. PDF

    Topics Physics · Shared terms “scalar field”, “imposing”

  7. Aspects of the Classical Double Copy

    Rashid Alawadhi PDF

    Topics Physics · Shared terms “Einstein”

  8. Navigating string theory field space with geometric flows

    Saskia Demulder, Dieter Lust and Thomas Raml PDF

    Topics Physics · Shared terms “scalar field”, “Distance Conjecture”, “geometric flows”

Read around it

Background reading

The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.

Ricci flow Hamilton's Ricci flow evolves a Riemannian metric by minus twice its Ricci curvature. It is a nonlinear heat equation for geometry: it spreads… Start with: Three-manifolds with positive Ricci curvature (Hamilton, 1982) Physics Ricci flow first appeared in physics, as the leading-order renormalization-group flow of the string sigma model (Friedan, 1980). Start with: Nonlinear Models in 2+ε Dimensions (Friedan, 1980)

In the guidebook

  1. 5A.5
    Uniformization and the Two-Dimensional Ricci FlowBook 5A · Complex Analysis and Conformal Geometry

    Constant-curvature metrics on surfaces, and Ricci flow as a heat equation for the conformal factor.

  2. 10A.12
    Curve Shortening and Minimal DiscsBook 10A · Three-Manifolds and Geometrization

    How loops shrink under curvature, how the discs they bound lose area, and Perelman's extinction estimate.

  3. 11A.1
    The Equation and Its First SolutionsBook 11A · The Ricci Flow: Existence and Maximum Principles

    A heat equation for the metric: spheres, cylinders and scaling.