Paper · May 3, 2019

Topology-changing horizons at large D as Ricci flows

Roberto Emparan, Ryotaku Suzuki

hep-tharXiv:1905.01062v3
View PDF View HTML arXiv page

As on arXiv

Abstract

The topology-changing transition between black strings and black holes localized in a Kaluza-Klein circle is investigated in an expansion in the inverse of the number of dimensions D. Performing a new kind of large-D scaling reduces the problem to a Ricci flow of the near-horizon geometry as it varies along the circle direction. The flows of interest here simplify to a non-linear logarithmic diffusion equation, with solutions known in the literature which are interpreted as the smoothed conifold geometries involved in the transition, namely, split and fused cones, which connect to black holes and non-uniform black strings away from the conical region. Our study demonstrates the adaptability of the 1/D expansion to deal with all the regimes and aspects of the static black hole/black string system, and provides another instance of the manner in which the large D limit reduces the task of solving Einstein's equations to a simpler but compelling mathematical problem.

View PDF View HTML arXiv page
Submitted
May 3, 2019
Last revised
Jul 22, 2019 (v3)
Subjects
hep-th, gr-qc
Journal
JHEP 07 (2019) 094
DOI
10.1007/JHEP07(2019)094

Comments: 34 pages, 7 figures; v2: minor corrections, refs added; v3: minor corrections, some comments added

Ricci flowPhysics

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 Parametric Solution of a Small-Large Black Hole Coexistence Curve (Shanshan Li, Dan-Dan Li, Li-Qin Mi et al., 2017)2Li 2017 Extended Phase Space Thermodynamics of Black Holes in Massive Gravity (Parthapratim Pradhan, 2018)8Pradhan 2018 Geometric Flow Equations for Schwarzschild-AdS Space-time and Hawking-Page Phase Transition (Davide De Biasio and Dieter Lust, 2020)3De Biasio 2020 Stochastic Quantization of General Relativity à la Ricci-Flow (Matteo Lulli, Antonino Marciano and Xiaowen Shan, 2021)4Lulli 2021 Gradient flow of Einstein-Maxwell theory and Reissner-Nordström black holes (Davide De Biasio, Julian Freigang, Dieter Lust et al., 2022)1De Biasio 2022 On curvature related geometric properties of Hayward black hole spacetime (Absos Ali Shaikh, Shyamal Kumar Hui, Biswa Ranjan Datta et al., 2023)7Shaikh 2023 Noise-induced stabilization of Schwarzschild–AdS black holes under stochastic Ricci flow (Jihui Wang, Matteo Lulli and Antonino Marciano, 2026)6Wang 2026 Conformal-Mapping Method for Horizon Multipoles in Numerical Relativity: Implementation, Kerr Validation, and Applications Beyond Axisymmetry (Yeong-Bok Bae, Young-Hwan Hyun and Gungwon Kang, 2026)5Bae 2026
Closer to the centre: more closely connected. Clockwise from the top: oldest to newest. Ricci flowWider flowsalso connected to each other
  1. Gradient flow of Einstein-Maxwell theory and Reissner-Nordström black holes

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

    Topics Physics · Shared terms “black hole”, “horizon geometry”, “direction”

  2. Parametric Solution of a Small-Large Black Hole Coexistence Curve

    Shanshan Li, Dan-Dan Li, Li-Qin Mi et al.

    Topics Physics · Shared terms “black hole”, “transition”

  3. Geometric Flow Equations for Schwarzschild-AdS Space-time and Hawking-Page Phase Transition

    Davide De Biasio and Dieter Lust

    Topics Physics · Shared terms “black hole”, “transition”

  4. Stochastic Quantization of General Relativity à la Ricci-Flow

    Matteo Lulli, Antonino Marciano and Xiaowen Shan

    Topics Physics · Shared terms “black hole”, “Einstein equations”

  5. Conformal-Mapping Method for Horizon Multipoles in Numerical Relativity: Implementation, Kerr Validation, and Applications Beyond Axisymmetry

    Yeong-Bok Bae, Young-Hwan Hyun and Gungwon Kang

    Topics Physics · Shared terms “black hole”, “horizon geometry”

  6. Noise-induced stabilization of Schwarzschild–AdS black holes under stochastic Ricci flow

    Jihui Wang, Matteo Lulli and Antonino Marciano

    Topics Physics · Shared terms “black hole”

  7. On curvature related geometric properties of Hayward black hole spacetime

    Absos Ali Shaikh, Shyamal Kumar Hui, Biswa Ranjan Datta et al.

    Topics Physics · Shared terms “black hole”

  8. Extended Phase Space Thermodynamics of Black Holes in Massive Gravity

    Parthapratim Pradhan

    Topics Physics · Shared terms “black hole”, “transition”

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.