Related papers: The Hawking energy on photon surfaces
We introduce new systems of PDE on initial data sets $(M,g,k)$ whose solutions model double-null foliations. This allows us to generalize Geroch's monotonicity formula for the Hawking mass under inverse mean curvature flow to initial data…
The boundary of any observer's spacetime is the boundary that divides what the observer can see from what they cannot see. The boundary of an observer's spacetime in the presence of a black hole is not the true (future event) horizon of the…
In [8] Gerhardt proves longtime existence for the inverse mean curvature flow in globally hyperbolic Lorentzian manifolds with compact Cauchy hypersurface, which satisfy three main structural assumptions: a strong volume decay condition, a…
It is pointed out that the entropy of a membrane which is quantized perturbatively around a background position of fixed radius in a black hole spacetime is equal to the Bekenstein-Hawking entropy, if 1) the membrane surface is the horizon…
We prove Harnack inequalities for hypersurfaces flowing on the unit sphere by $p$-powers of a strictly monotone, 1-homogeneous, convex, curvature function $f$, $0<p\leq 1.$ If $f$ is the mean curvature, we obtain stronger Harnack…
The 3+1 Hamiltonian formulation in the gauge $D_tN=-K$ on the lapse function fixes the direction of time associated with the trace $K$ of the extrinsic curvature tensor. The Hamiltonian equations hereby become hyperbolic. We study this new…
In this paper, we study fully nonlinear curvature flows of noncompact spacelike hypersurfaces in Minkowski space. We prove that if the initial hypersurface satisfies certain conditions, then the flow exists for all time. Moreover, we show…
Recent advances in observational cosmology are changing the way we view the nature of time. In general relativity, the freedom in choosing a time hypersurface has hampered the implementation of the theory. Fortunately, Hamilton-Jacobi…
This note introduces a notion of entropy for submanifolds of hyperbolic space analogous to the one introduced by Colding and Minicozzi for submanifolds of Euclidean space. Several properties are proved for this quantity including…
If general relativity is spontaneously induced, the black hole limit is governed by a phase transition which occurs precisely at the would have been horizon. The exterior Schwarzschild solution then connects with a novel core of vanishing…
In this paper we prove a monotonicity formula for the integral of the mean curvature for complete and proper hypersurfaces of the hyperbolic space and, as consequences, we obtain a lower bound for the integral of the mean curvature and that…
We show that "particle production" by gravitational field, especially the Hawking effect, may be treated as some quantum inertial effect, with the energy of Hawking radiation as some vacuum energy shift. This quantum inertial effect is…
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…
By making use of the nice behavior of Hawking masses of slices of a weak solution of inverse mean curvature flow in three dimensional asymptotically hyperbolic manifolds, we are able to show that each slice of the flow is star-shaped after…
This paper is devoted to the study of curvature properties of Hayward black hole (briefly, HBH) spacetime, which is a solution of Einstein field equations (briefly, EFE) having non-vanishing cosmological constant. We have proved that the…
We investigate photon surfaces and their stability in a less symmetric spacetime, a general static warped product with a warping function acting on a Riemannian submanifold of codimension two. We find a one-dimensional pseudopotential that…
In this second part of our series of two papers, where spacetime is modelled by a graph, where Planck size quantum black holes lie on the vertices, we consider the thermodynamics of spacetime. We formulate an equation which tells in which…
We prove a conjecture of Bernstein that the superconvexity of the heat kernel on hyperbolic space holds in all dimensions and, hence, there is an analog of Huisken's monotonicity formula for mean curvature flow in hyperbolic space of all…
Here we consider a scenario in which dark energy is associated with the apparent area of a surface in the early universe. In order to resemble the cosmological constant at late times, this hypothetical reference scale should maintain an…
We introduce the shifted inverse curvature flow in hyperbolic space. This is a family of hypersurfaces in hyperbolic space expanding by $F^{-p}$ with positive power $p$ for a smooth, symmetric, strictly increasing and $1$-homogeneous…