相关论文: The crease flow on null hypersurfaces
We carried out numerical calculations of a contribution of the waterfall field to the primordial curvature perturbation (on uniform density hypersurfaces) $\zeta$, which is produced during waterfall transition in hybrid inflation scenario.…
The superfluid phase transition dynamics and associated spontaneous vortex formation with the crossing of the critical temperature in a disk geometry is studied in the framework of the $AdS/CFT$ correspondence by solving the…
The theory of integrable systems of Hamiltonian PDEs and their near-integrable deformations is used to study evolution equations resulting from vertical-averages of the Euler system for two-layer stratified flows in an infinite 2D channel.…
We consider the Whitham equations for deformations of hyperelliptic spectral curves, which preserve all periods of a meromorphic differential. If the meromorphic differential has a root at a fixed point of the hyperelliptic involution, then…
We study the length-preserving elastic flow of curves in arbitrary codimension with free boundary on hypersurfaces. This constrained gradient flow is given by a nonlocal evolution equation with nonlinear higher-order boundary conditions. We…
Acoustic waves in fluids undergoing the transition from sub- to supersonic flow satisfy governing equations similar to those for light waves in the immediate vicinity of a black hole event horizon. This acoustic analogy has been used by…
By applying the dimensionless scheme, we investigate the quasinormal modes and phase transitions analytically for three types of regular black holes. The universal deviations to the first law of mechanics in regular black holes are proved.…
In this paper, we produce explicit examples of mean curvature flow of (2m-1)-dimensional submanifolds which converge to (2m-2)-dimensional submanifolds at a finite time. These examples are a special class of hyperspheres in $\mathbb{C}^{m}$…
We consider the inverse mean curvature flow by parallel hypersurfaces in space forms. We show that such a flow exists if and only if the initial hypersurface is isoparametric. The flow is characterized by an algebraic equation satisfied by…
We discuss the branching structure of the quantum-gravitational wave function that describes the evaporation of a black hole. A global wave function which initially describes a classical Schwarzschild geometry is continually decohered into…
A generic black hole merger occurs through a restructuring of creases (sharp edges) on the event horizon. This process is studied for a black hole merger in the limit of infinite mass ratio, for which constructing the event horizon reduces…
We consider the holographic hydrodynamics of black holes in generally covariant gravity theories with a preferred time foliation. Gravitational perturbations in these theories have spin two and spin zero helicity modes with generically…
We prove that the 3-D free-surface incompressible Euler equations with regular initial geometries and velocity fields have solutions which can form a finite-time "splash" (or "splat") singularity first introduced in [9], wherein the…
We consider the evolution of fronts by mean curvature in the presence of obstacles. We construct a weak solution to the flow by means of a variational method, corresponding to an implicit time-discretization scheme. Assuming the regularity…
Stationary, inviscid, axi-symmetric, rotating, transonic accretion flow has been studied in a general relativistic framework, in the Schwarzschild metric; for three different flow geometries - under both polytropic and isothermal…
We analyze the steady radial accretion of matter into a nonrotating black hole. Neglecting the self-gravity of the accreting matter, we consider a rather general class of static, spherically symmetric and asymptotically flat background…
In this paper, we consider the evolution of spacelike graphic hypersurfaces defined over a convex piece of hyperbolic plane $\mathscr{H}^{n}(1)$, of center at origin and radius $1$, in the $(n+1)$-dimensional Lorentz-Minkowski space…
We introduce a formulation of Eulerian general relativistic hydrodynamics which is applicable for (perfect) fluid data prescribed on either spacelike or null hypersurfaces. Simple explicit expressions for the characteristic speeds and…
Let $(\mathbf{M}^{3},J,\theta_{0})$ be a closed pseudohermitian 3-manifold. Suppose the associated torsion vanishes and the associated $Q$-curvature has no kernel part with respect to the associated Paneitz operator. On such a background…
We construct a general relativistic model for the accretion flow of a rotating finite cloud of non-interacting particles infalling onto a Schwarzschild black hole. The streamlines start at a spherical shell, where boundary conditions are…