Paper · Feb 15, 2021

Masking singularities in Weyl gravity and Ricci flows

Vladimir Dzhunushaliev, Vladimir Folomeev

gr-qcarXiv:2102.07494v2
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Abstract

Within vacuum Weyl gravity, we obtain a solution by which, using different choices of the conformal factor, we derive metrics describing (i) a bounce of the universe; (ii) toroidal and spherical wormholes; and (iii) a change in metric signature. It is demonstrated that singularities occurring in these systems are "masked". We give a simple explanation of the possibility of masking the singularities within Weyl gravity. It is shown that in the first and third cases the three-dimensional metrics form Ricci flows. The question of the possible applicability of conformal Weyl gravity as some phenomenological theory in an approximate description of quantum gravity is discussed.

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Submitted
Feb 15, 2021
Last revised
Apr 27, 2021 (v2)
Subjects
gr-qc
DOI
10.1140/epjc/s10052-021-09188-4

Comments: 10 pages

Ricci flowSingularities3-manifoldsPhysics

Its neighbourhood

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 2016, 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 Evolution and metric signature change of maximally symmetric spaces under the Ricci flow (R. Cartas-Fuentevilla, A. Herrera-Aguilar and J. A. Olvera-Santamaría, 2017)2Cartas-Fuent 2017 Cosmology from the two-dimensional renormalization group acting as the Ricci flow (Daniel Friedan, 2019)4Friedan 2019 Swampland, Gradient Flow and Infinite Distance (Alex Kehagias, Dieter Lust and Severin Lüst, 2019)7Kehagias 2019 Perelman's Ricci Flow in Topological Quantum Gravity (Alexander Frenkel, Petr Horava and Stephen Randall, 2020)8Frenkel 2020 Brownian Motion in the Hilbert Space of Quantum States along with the Ricci Flow and Stochastically Emergent Einstein-Hilbert Action: Formulating a Well-Defined Feynman Path-Integral Measure for Quantum Fields in the Presence of Gravity (A. A. Varshovi, 2022)1Varshovi 2022 A Statistical Fields Theory underlying the Thermodynamics of Ricci Flow and Gravity (M. J. Luo, 2023)3Luo 2023 A path integral formula of quantum gravity emergent from entangled local structures (Jinglong Liu, Stephon Alexander, Antonino Marciano et al., 2023)5Liu 2023 The perturbative Ricci flow in gravity (Robert V. Harlander, Yannick Kluth, Jonas T. Kohnen et al., 2026)6Harlander 2026
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Brownian Motion in the Hilbert Space of Quantum States along with the Ricci Flow and Stochastically Emergent Einstein-Hilbert Action: Formulating a Well-Defined Feynman Path-Integral Measure for Quantum Fields in the Presence of Gravity

    A. A. Varshovi

    Topics Physics, 3-manifolds · Shared terms “universe”

  2. Evolution and metric signature change of maximally symmetric spaces under the Ricci flow

    R. Cartas-Fuentevilla, A. Herrera-Aguilar and J. A. Olvera-Santamaría

    Topics Physics, 3-manifolds · Shared terms “metric signature”

  3. A Statistical Fields Theory underlying the Thermodynamics of Ricci Flow and Gravity

    M. J. Luo

    Topics Physics, 3-manifolds

  4. Cosmology from the two-dimensional renormalization group acting as the Ricci flow

    Daniel Friedan

    Topics Physics, 3-manifolds, Singularities · Shared terms “universe”

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

    Jinglong Liu, Stephon Alexander, Antonino Marciano et al.

    Topics Physics · Shared terms “quantum gravity”

  6. The perturbative Ricci flow in gravity

    Robert V. Harlander, Yannick Kluth, Jonas T. Kohnen et al.

    Topics Physics

  7. Swampland, Gradient Flow and Infinite Distance

    Alex Kehagias, Dieter Lust and Severin Lüst

    Topics Physics · Shared terms “quantum gravity”, “discussed”

  8. Perelman's Ricci Flow in Topological Quantum Gravity

    Alexander Frenkel, Petr Horava and Stephen Randall

    Topics Physics · Shared terms “quantum gravity”

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) Singularities On a closed manifold the flow can stop in finite time: curvature blows up, often because a neck pinches off. Start with: The formations of singularities in the Ricci Flow (Hamilton, 1993) 3-manifolds Dimension three is where Ricci flow has done its most complete work. It proves geometrization, describes the flow's long-time behaviour, and now… 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. 11B.4
    Blow-Ups, Blow-Downs and Splitting at InfinityBook 11B · Solitons, Compactness and Singularities

    Limits of rescaled manifolds and flows: why blow-up limits are nonnegatively curved, what blow-downs see, and how lines appear at infinity.

  2. 11B.6
    Rotationally Symmetric Flows and the Standard SolutionBook 11B · Solitons, Compactness and Singularities

    The neckpinch in equations: warped products under the flow, what the maximum principle forces, and the standard solution that surgery glues in.

  3. 10A.1
    A Zoo of Three-ManifoldsBook 10A · Three-Manifolds and Geometrization

    The 3-sphere, lens spaces, the Poincaré sphere, the Hopf fibration and the shape of space.