Related papers: Proper projective collineation in non-static spher…
An overview of recent developments in the renormalization and in the implementation of spacetime symmetries of noncommutative field theory is presented, and argued to be intimately related.
Here we explore the geometry of the osculating spaces to projective varieties of arbitrary dimension. In particular, we classify varieties having very degenerate higher order osculating spaces and we determine mild conditions for the…
We introduce a new class of out-of-equilibrium noninteracting topological phases, the topological space-time crystals. These are time-dependent quantum systems which do not have discrete spatial translation symmetries, but instead are…
Generalizing the Lie derivative of smooth tensor fields to distribution-valued tensors, we examine the Killing symmetries and the collineations of the curvature tensors of some distributional domain wall geometries. The chosen geometries…
Einstein's field equations for spatially self-similar spherically symmetric perfect-fluid models are investigated. The field equations are rewritten as a first-order system of autonomous differential equations. Dimensionless variables are…
We argue that a particular spacetime, a spherically symmetric spacetime with hyper-surface orthogonal, radial, homothetic Killing vector, is a physically meaningful spacetime that describes the problem of spherical gravitational collapse in…
A general relativistic description of a disk rotating at constant angular velocity is given. It is argued that conceptually this direct approach poses fewer problems than the special relativistic one. For observers on the disk, the geometry…
Having developed a description of indefinite extrinsic symmetric spaces by corresponding infinitesimal objects in the preceding paper we now study the classification problem for these algebraic objects. In most cases the transvection group…
Non-relativistic particles that are effectively confined to two dimensions can in general move on curved surfaces, allowing dynamical phenomena beyond what can be described with scalar potentials or even vector gauge fields. Here we…
Three natural classes of orthonormal frames, namely Frenet-Serret, Fermi-Walker and parallel transported frames, exist along any timelike world line in spacetime. Their relationships are investigated for timelike circular orbits in…
Considering homogeneous four-dimensional space-time geometries within real projective geometry provides a mathematically well-defined framework to discuss their deformations and limits without the appearance of coordinate singularities. On…
We study integral geometric properties of non-compact harmonic spaces.
We discover a class of spacetime symmetries unique to time-periodic systems, which we term "mixing symmetry" due to its combination of space and time coordinates in the symmetry transformation. We systematically enumerate the symmetry…
We study a class of static spherically symmetric vacuum solutions in modified teleparallel gravity solving the field equations for a specific model Ansatz, requiring the torsion scalar $T$ to be constant. We discuss the models falling in…
We show that the spacetimes of domain wall solutions to the coupled Einstein-scalar field equations with a given scalar field potential fall into two classes, depending on whether or not reflection symmetry on the wall is imposed. Solutions…
We prove a symmetric version of B\'ezout's theorem. More precisely, we show that the symmetric orbit type of a transverse intersection of complex symmetric hypersurfaces in projective space is determined by the degrees. In the projective…
We study the condition for the appearance of space-time supercharges in twisted sectors of asymmetric orbifold models. We present a list of the asymmetric $Z_N$-orbifold models which satisfy a simple condition necessary for the appearance…
Focus of this study is to explore some aspects of mathematical foundations for using complex manifolds as a model for space-time. More specifically, certain equations of motions have been derived as a Projective geodesic on a real manifold…
We present a local classification of smooth projective surfaces in 3-space via projective transformations in accordance with singularity types of central projections up to codimension 4. We also discuss relations between our classification…
In this work, exact solutions of static and spherically symmetric space-times are analyzed in f(R) modified theories of gravity coupled to nonlinear electrodynamics. Firstly, we restrict the metric fields to one degree of freedom,…