Related papers: Cauchy Horizon Endpoints and Differentiability
The horizon is a classical concept that arises in general relativity, and is therefore not clearly defined when the source cannot be reliably described by classical physics. To any (sufficiently) localised quantum mechanical wave-function,…
A thorough classification of the topologies of compact homogeneous universes is given except for the hyperbolic spaces, and their global degrees of freedom are completely worked out. To obtain compact universes, spatial points are…
While the topology of the space of all smooth immersed curves on the $2$-sphere $\mathbb{S}^2$ that start and end at given points in given directions is well known, it is an open problem to understand the homotopy type of its subspaces…
It is shown that Kundt's metric for vacuum cannot be constructed when two-dimensional space-like sections of null hypersurfaces are compact, connected manifolds with no boundary unless they are tori or spheres, i.e. higher genus $\mathbf{g}…
While self-similar sets have no tangents at any single point, self-affine curves can be smooth. We consider plane self-affine curves without double points and with two pieces. There is an open subset of parameter space for which the curve…
We generalize the concept of complexity near horizons to all nondegenerate black holes. For Schwarzschild black holes, we show that Rindler observers see a complexity change of $S$ during proper time $1/\kappa$ which corresponds to the…
We investigate the possibility of having an event horizon within several classes of metrics that asymptote to the maximally supersymmetric IIB plane wave. We show that the presence of a null Killing vector (not necessarily covariantly…
To implement the consistent black hole complementarity principle, we need two assumptions: first, there exists a singularity near the center, and second, global horizons are the same as local horizons. However, these assumptions are not…
Several sets of radially propagating null congruence generators are exploited in order to form 3-dimensional marginally trapped surfaces, referred to as black hole and cosmological apparent horizons in a Horava universe. Based on this…
We present a quantum theory of black hole (and other) horizons, in which the standard assumptions of complementarity are preserved without contradicting information theoretic considerations. After the scrambling time, the quantum mechanical…
We study numerically the evolution of spactime, and in particular of a spacetime singularity, inside a black hole under a class of perturbations of non-compact support. We use a very simplified toy model of a spherical charged black hole…
The existence of a nowhere zero real vector field implies a well-known restriction on a compact manifold. But all manifolds admit nowhere zero complex vector fields. The relation between these observations is clarified.
We point out a simple construction of an infinite class of Einstein near-horizon geometries in all odd dimensions greater than five. Cross-sections of the horizons are inhomogeneous Sasakian metrics (but not Einstein) on S^3xS^2 and more…
Generic spherically symmetric self-similar collapse results in strong naked-singularity formation. In this paper we are concerned with particle creation during a naked-singularity formation in spherically symmetric self-similar collapse…
Null infinity arises as a boundary of the Penrose conformal completion of an asymptotically flat physical space-time. We first note that null infinity is a weakly isolated horizon (WIH), and then show that its familiar properties can be…
We construct a Banach space satisfying that the nearest point map (also called proximity mapping or metric projection) onto any compact and convex subset is continuous but not uniformly continuous. The space we construct is locally…
The use of "handy singularities" (i.e. singularities similar to those arising in the Deutch-Politzer space) enables one to avoid (almost) all known difficulties inherent usually to creation of time machines. A simple method is discussed for…
The Endpoint Theorem links the existence of a sequence (curve), without accumulation points, in a manifold to the existence of an open embedding of that manifold so that the image of the given sequence (curve) has a unique endpoint. It…
The theory of General Relativity predicts that black holes are a natural constituent of our Universe. Before a black hole binary relaxes to a final state, it undergoes damped oscillations which completely characterize the final object.…
We study the massless scalar field on asymptotically flat spacetimes with closed timelike curves (CTC's), in which all future-directed CTC's traverse one end of a handle (wormhole) and emerge from the other end at an earlier time. For a…