Related papers: Blackfolds, Plane Waves and Minimal Surfaces
A generic feature of nearly out-of-equilibrium dissipative systems is that they resonate through a set of quasinormal modes. Black holes - the absorbing objects par excellence - are no exception. When formed in a merger, black holes vibrate…
We perform a thorough study of greybody factors for minimally-coupled scalar fields propagating on the background of rotating black holes in higher (odd) dimensions with all angular momenta set equal. For this special case, the solution…
Schwarzschild-de Sitter (SdS) black holes do not admit a completely smooth Euclidean continuation. We discuss some modifications of the gravitational path integral that give Euclidean SdS a semiclassical equilibrium interpretation. First we…
It is known from the work of Banados et al. that a space-time with event horizons (much like the Schwarzschild black hole) can be obtained from 2+1 dimensional anti-de Sitter space through a suitable identification of points. We point out…
We consider the optical appearance of a non-singular, spherically symmetric black hole from Eddington-inspired Born-Infeld gravity coupled to anisotropic fluids. Such a black hole has a single (external) horizon located very near the…
On a class of dynamical spacetimes which are asymptotic as $t\to\infty$ to a stationary spacetime containing a horizon $\mathcal{H}_0$, we show the existence of a unique null hypersurface $\mathcal{H}$ which is asymptotic to…
The requirement that a trapped spacetime domain forms in finite time for distant observers is logically possible and sometimes unavoidable, but its consequences are not yet fully understood. In spherical symmetry, the characterization of…
A submanifold $M^m$ of a Euclidean space $R^{m+p}$ is said to have harmonic mean curvature vector field if $\Delta \vec{H}=0$, where $\vec{H}$ is the mean curvature vector field of $M\hookrightarrow R^{m+p}$ and $\Delta$ is the rough…
We study the collapse of a thin dust shell from the point of view of the horizon dynamics. We identify the critical surfaces at which time and space coordinates interchange their roles and investigate their properties by using the formalism…
Minimal surfaces arise as energy minimizers for fluid membranes and are thus found in a variety of biological systems. The tight lamellar structures of the endoplasmic reticulum and plant thylakoids are composed of such minimal surfaces in…
Consider an orientable compact surface in three dimensional Euclidean space with minimum total absolute curvature. If the Gaussian curvature changes sign to finite order and satisfies a nondegeneracy condition along closed asymptotic…
We show that in presence of a cosmological constant or, more generally, of a scalar potential, there can exist actually more possibilities for the horizon geometry of a four-dimensional black hole than the hitherto known spherical,…
We construct topological invariants, called abstract weak orbit spaces, of flows and homeomorphisms on topological spaces, to describe both gradient dynamics and recurrent dynamics. In particular, the abstract weak orbit spaces of flows on…
It has recently been shown that a stationary, asymptotically flat vacuum black hole in five space-time dimensions with two commuting axial symmetries must have an event horizon with either a spherical, ring or lens-space topology. In this…
In a recent paper (gr-qc/0509107) the author and Rick Schoen obtained a generalization to higher dimensions of a classical result of Hawking concerning the topology of black holes. It was proved that, apart from certain exceptional…
Trumpet geometries play an important role in numerical simulations of black hole spacetimes, which are usually performed under the assumption of asymptotic flatness. Our Universe is not asymptotically flat, however, which has motivated…
Let $\alpha\in\r$ and let $\vec{v}\in\r^3$ be a unit vector. A singular minimal surface $\Sigma$ in Euclidean space is a surface $\Sigma$ whose mean curvature $H$ satisfies $H=\alpha\frac{\langle N,\vec{v}\rangle}{\langle…
Manifold reconstruction has been extensively studied for the last decade or so, especially in two and three dimensions. Recently, significant improvements were made in higher dimensions, leading to new methods to reconstruct large classes…
Minimal surfaces in closed 3-manifolds are classically constructed via the Almgren-Pitts approach. The Allen-Cahn approximation has proved to be a powerful alternative, and Chodosh and Mantoulidis (in Ann. Math. 2020) used it to give a new…
In a companion paper [1], we have presented a cross-correlation approach to near-horizon physics in which bulk dynamics is probed through the correlation of quantities defined at inner and outer spacetime hypersurfaces acting as test…