Related papers: When is the Hawking mass monotone under Geometric …

We study a volume preserving curvature flow of convex hypersurfaces, driven by a power of the $k$-th elementary symmetric polynomial in the principal curvatures. Unlike most of the previous works on related problems, we do not require…

This paper concerns closed hypersurfaces of dimension $n(\geq 2)$ in the hyperbolic space ${\mathbb{H}}_{\kappa}^{n+1}$ of constant sectional curvature $\kappa$ evolving in direction of its normal vector, where the speed is given by a power…

Motivated by the conjectured Penrose inequality and by the work of Hawking, Geroch, Huisken and Ilmanen in the null and the Riemannian case, we examine necessary conditions on flows of two-surfaces in spacetime under which the Hawking…

In this paper, we consider the mean curvature flow of convex hypersurfaces in Euclidean spaces with a general forcing term. We show that the flow may shrink to a point in finite time if the forcing term is small, or exist for all times and…

We consider deformation of the d+2 dimensional asymptotically flat Schwarzschild black hole spacetime with the induced metric on a d-sphere at $r=r_c$ held fixed. This is done without taking the near horizon limit. The deformation is…

We consider the problem of determination of a volume of some bounded space-like hypersurfaces in the case of spherically symmetric spacetimes. In the case when the hypersurfaces is cut or bounded by a light-like hypersurface the problem may…

In black hole evaporation process, the mass of the hole anti-correlates with the Hawking temperature. This indicates that the smaller holes have higher surface gravity. For analogue Hawking effects, however, the acoustic surface gravity is…

It is a deceptively simple question to ask how acoustic disturbances propagate in a non-homogeneous flowing fluid. This question can be answered by invoking the language of Lorentzian differential geometry: If the fluid is barotropic and…

We study the Hawking effect in terms of the geometric phase acquired by a two-level atom as a result of coupling to vacuum fluctuations outside a Schwarzschild black hole in a gedanken experiment. We treat the atom in interaction with a…

Time-independent Hamiltonian flows are viewed as geodesic flows in a curved manifold, so that the onset of chaos hinges on properties of the curvature two-form entering into the Jacobi equation. Attention focuses on ensembles of orbit…

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…

Although previous results have ruled out the possibility of a static horizon in cosmology, we present black hole and white hole metrics that retain static horizons while reproducing cosmological behavior at large distances. Using an…

We construct the gravitational dual of a one-parameter class of states of strongly coupled $SU(N)$ $\mathcal{N}=4$ SYM at infinite $N$ and asymptotic temperature $T_{\infty}$, on a fixed Schwarzschild black hole background with temperature…

In this paper, we study a class of non-homogeneous anisotropic fully nonlinear curvature flows in $\mathbb{R}^{n+1}$. More precisely, we consider a hypersurface $M$ in $\mathbb{R}^{n+1}$ deformed by a flow along its unit normal with its…

The {\it curvature} and the {\it reduced curvature} are basic differential invariants of the pair: (Hamiltonian system, Lagrange distribution) on the symplectic manifold. We show that negativity of the curvature implies that any bounded…

This paper gives some examples of hypersurfaces $\phi_t(M^n)$ evolving in time with speed determined by functions of the normal curvatures in an $(n+1)$-dimensional hyperbolic manifold; we emphasize the case of flow by harmonic mean…

In 2004, Manning showed that the topological entropy of the geodesic flow of a closed surface of non-constant negative curvature is strictly decreasing along the normalized Ricci flow, and he asked if an analogous result holds in higher…

We consider the Yang-Mills flow on hyperbolic 3-space. The gauge connection is constructed from the frame-field and (not necessarily compatible) spin connection components. The fixed points of this flow include zero Yang-Mills curvature…

We define a mass function on asymptotically hyperbolic manifolds with continuous metrics via the normalized Ricci DeTurck flow. This definition coincides with the classical mass for smooth metrics. We also introduce the scalar curvature…

In this paper we discuss the stability of geodesic spheres in $\mathbb{S}^{n+1}$ under constrained curvature flows. We prove that under some standard assumptions on the speed and weight functions, the spheres are stable under perturbations…