Related papers: A note on the uniqueness of global static decompos…
We give a short proof of a result of Jordan and Tanigawa that a 4-connected graph which has a spanning planar triangulation as a proper subgraph is generically globally rigid in R^3. Our proof is based on a new sufficient condition for the…
In this paper, we establish that a four-dimensional static vacuum asymptotically flat spacetime containing a massive particle sphere is isometric to the Schwarzschild spacetime. Our results expand upon existing uniqueness theorems for…
Let $D$ be a set of smooth vector fields on the smooth manifold $M$.It is known that orbits of $D$ are submanifolds of M. Partition $F$ of M into orbits of $D$ is a singular foliation. In this paper we are studying geometry of foliation…
We develop a criterion for a point of global function field to be a unique wild point of some self-equivalence of this field. We show that this happens if and only if the class of the point in the Picard group of the field is $2$-divisible.…
Given an d-dimensional manifold with two commuting Killing vectors, together with an d - 1 dimensional submanifold in which one of the Killing vectors lies, then the lapse and shift of the second Killing vector, relative to this slice,…
The nature of the initial singularity in spatially compact plane symmetric scalar field cosmologies is investigated. It is shown that this singularity is crushing and velocity dominated and that the Kretschmann scalar diverges uniformly as…
We show that for three dimensional space-times admitting a hypersurface orthogonal Killing vector field Deser, Jackiw and Templeton's vacuum field equations of topologically massive gravity allow only the trivial flat space-time solution.…
A physical applicability of normed split-algebras, such as hyperbolic numbers, split-quaternions and split-octonions is considered. We argue that the observable geometry can be described by the algebra of split-octonions. In such a picture…
Cylindrically symmetric static manifolds are classified according to their homotheties and metrics. In each case the homothety vector fields and the corresponding metrics are obtained explicitly by solving the homothety equations. It turns…
The limiting slow dynamics of slow-fast, piecewise-linear, continuous systems of ODEs occurs on critical manifolds that are piecewise-linear. At points of non-differentiability, such manifolds are not normally hyperbolic and so the…
We consider general relativity with cosmological constant minimally coupled to the electromagnetic field and assume that the four-dimensional space-time manifold is a warped product of two surfaces with Lorentzian and Euclidean signature…
We present a new approach to the study of vacuum spacetimes with a Killing symmetry. The central quantity in this approach is the exterior derivative of the Killing vector field, which is a test electromagnetic field. Considering the…
We review the mathematical framework necessary to understand the physical content of quantum singularities in static spacetimes. We present many examples of classical singular spacetimes and study their singularities by using wave packets…
The vorticity of a vector field on 3-dimensional Euclidean space is usually given by the curl of the vector field. In this paper, we extend this concept to n-dimensional compact and oriented Riemannian manifold. We analyse many properties…
In the guiding center theory, smooth unit vectors perpendicular to the magnetic field are required to define the gyrophase. The question of global existence of these vectors is addressed using a general result from the theory of…
We prove that a singular complex surface that admits a complete holomorphic vector field that has no invariant curve through a singular point of the surface is obtained from a Kato surface by contracting some divisor (in particular, it is…
We study the global structure of Lorentzian manifolds with partial sectional curvature bounds. In particular, we prove completeness theorems for homogeneous and isotropic cosmologies as well as static spherically symmetric spacetimes. The…
The study of dynamic singularity formation in spacetime, focusing on scalar field collapse models, is analysed. We revisit key findings regarding open spatial topologies, concentrating on minimal conditions necessary for singularity and…
Under the natural action of the pure mapping class group of a surface of genus at least three, we show that any global fixed point in the low-dimensional deformation space of the surface group corresponds to the trivial representation. A…
Given a space-time $(\mathscr{M}, g_{ab})$ admitting a dynamical horizon segment (DHS) $\mathscr{H}$, we show that there are stringent constraints on the Killing fields $\xi^a$ that $g_{ab}$ can admit in a neighborhood of $\mathscr{H}$:…