Related papers: Ricci flows, wormholes and critical phenomena
We present a new relation between the short time behavior of the heat flow, the geometry of optimal transport and the Ricci flow. We also show how this relation can be used to define an evolution of metrics on non-smooth metric measure…
We investigate the response of the traversable wormholes to the external perturbations through finding their characteristic frequencies and time-domain profiles. The considered solution describes traversable wormholes between the branes in…
Evolving Lorentzian wormholes with the required matter satisfying the Energy conditions are discussed. Several different scale factors are used and the corresponding consequences derived. The effect of extra, decaying (in time) compact…
Motivated by the newest progress in geometric flows both in mathematics and physics, we apply the geometric evolution equation to study some black-hole problems. Our results show that, under certain conditions, the geometric evolution…
This brief review discusses the existence conditions of wormhole throats and wormholes as global configurations in general relativity under the assumptions of cylindrical and axial symmetries. It is pointed out, in particular, that wormhole…
We present numerical visualizations of Ricci Flow of surfaces and 3-dimensional manifolds of revolution. Ricci_rot is an educational tool which visualizes surfaces of revolution moving under Ricci flow. That these surfaces tend to remain…
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…
By applying the theory of group-invariant solutions we investigate the symmetries of Ricci flow and hyperbolic geometric flow both on Riemann surfaces. The warped products on $\mathcal {S}^{n+1}$ of both flows are also studied.
The Ricci flow has been of fundamental importance in mathematics, most famously though its use as a tool for proving the Poincar\'e Conjecture and Thurston's Geometrization Conjecture. It has a parallel life in physics, arising as the first…
Ricci curvature and Ricci flow have proven to be powerful tools for analyzing the geometry of discrete structures, particularly on undirected graphs, where they have been applied to tasks ranging from community detection to graph…
Wormholes are a hypothetical object that connects disparate points in spacetime. It is a theoretically well-motivated black hole alternative and offers a potential observationally testable arena for probing strong-field gravity with…
This is a survey paper focusing on the interplay between the curvature and topology of a Riemannian manifold. The first part of the paper provides a background discussion, aimed at non-experts, of Hopf's pinching problem and the Sphere…
We analyze traversable wormholes defined by the dynamic line elements that asymptotically approaches Friedmann-Robertson-Walker (FRW) universe. This dynamical wormholes is supported by the galactic dark matter as well as perfect isotropic…
This article reports recent developments of the research on Hamilton's Ricci flow and its applications.
In this paper, we study the evolution of L2 p-forms under Ricci flow with bounded curvature on a complete non-compact or a compact Riemannian manifold. We show that under curvature pinching conditions on such a manifold, the L2 norm of a…
A geometric method, using the Ricci (or mean) curvature of the Lagrangian (configuration) manifold, is used to study the relative instability of evolving $N$-body gravitating systems with massive centres. The performed numerical experiments…
Thus far, the known wormholes in string theory connecting disjoint boundaries represented by finite volume quotients of hyperbolic spaces leak: they are non-perturbatively unstable towards brane-anti-brane nucleation in the flux backgrounds…
Exact solutions of traversable wormholes were recently found under the assumption of spherical symmetry and the existence of a non-static conformal symmetry. In this paper, we verify that in the case of the conformally symmetric spacetimes…
We extend to a theory of nonassociative geometric flows a string-inspired model of nonassociative gravity determined by star product and R-flux deformations. The nonassociative Ricci tensor and curvature scalar defined by (non) symmetric…
Giving explicit parametrizations of discrete constant Gaussian curvature surfaces of revolution that are defined from an integrable systems approach, we study Ricci flow for discrete surfaces, and see how discrete surfaces of revolution…