Related papers: Light-Cones, Almost Light-Cones and Almost-Complex…
This work is devoted to the relativistic generalization of Chasles' theorem, namely to the proof that every proper orthochronous isometry of Minkowski spacetime, which sends some point to its chronological future, is generated through the…
The concept of an $i$-symmetrization is introduced, which provides a convenient framework for most of the familiar symmetrization processes on convex sets. Various properties of $i$-symmetrizations are introduced and the relations between…
The indication from deep inelastic electron scattering experiments at SLAC that Bjorken scaling may really hold has motivated an extension of the hypotheses of current algebra to what may be called light-cone current algebra.
We consider Euclidean lattices spanned by images of algebraic conjugates of an algebraic number under Minkowski embedding, investigating their rank, properties of their automorphism groups and sets of minimal vectors. We are especially…
Spherically symmetric solutions in Brans-Dicke theory of relativity with zero coupling constant, $\omega=0$, are derived in the Schwarzschild line-element. The solutions are obtained from a cubic transition equation with one small…
Quasi-Exactly Solvable Schr\"odinger Equations occupy an intermediate place between exactly-solvable (e.g. the harmonic oscillator and Coulomb problems etc) and non-solvable ones. Their major property is an explicit knowledge of several…
A consistent set of asymptotic conditions for the simplest supergravity theory without cosmological constant in three dimensions is proposed. The canonical generators associated to the asymptotic symmetries are shown to span a…
This is a survey of some of the consequences of the recently introduced congruences on the theory of connectednesses (radical classes) and disconnectednesses (semisimple classes) of graphs and topological spaces. In particular, it is shown…
A recent refinement of Penrose's conformal framework for asymptotically flat space-times is summarized. The key idea concerns advanced and retarded conformal factors, which allow a rigid description of infinity as a locally metric light…
We show that the angular directions locally measured by a static geodesic observer in a generic cosmological background and expressed in the system of Fermi Normal Coordinates always coincide with those expressed in the Geodesic-Light-Cone…
We establish a gluing theorem for linearised vacuum gravitational fields in Bondi gauge on a class of characteristic surfaces in static vacuum four-dimensional backgrounds with cosmological constant $\Lambda \in \mathbb{R}$ and arbitrary…
If Einstein's equations are to describe a field theory of gravity in Minkowski spacetime, then causality requires that the effective curved metric must respect the flat background metric's null cone. The kinematical problem is solved using…
The paper focuses on the conformal Lorentz geometry of quasi-umbilical timelike surfaces in the $(1+2)$-Einstein universe, the conformal compactification of Minkowski 3-space realized as the space of oriented null lines through the origin…
Analytical computations in relativistic cosmology can be split into two sets: time evolution relating the initial conditions to the observer's light-cone and light propagation to obtain observables. Cosmological perturbation theory in the…
Classifying the zero-temperature ground states of quantum field theories with finite charge density is a very interesting problem. Via holography, this problem is mapped to the classification of extremal charged black brane geometries with…
Poincar\'e invariance is a well-tested symmetry of nature and sits at the core of our description of relativistic particles and gravity. At the same time, in most systems Poincar\'e invariance is not a symmetry of the ground state and is…
The lightlike geometry of codimension two spacelike submanifolds in Lorentz-Minkowski space has been developed in [Izumiya, S. and Romero Fuster, M. C. Selecta Mathematica (NS), 13 23--55 (2007)] which is a natural Lorentzian analogue of…
We demonstrate that the source of a shear-free null congruence is, generically, a world sheet of a singular string in the complex Minkowski space. In particular cases the string degenerates into the Newman's point singularity. We describe…
The relation between two branches of solutions (radiative and subradiative) of wave equations on Minkowski spacetime is investigated, for any integer spin, in flat Bondi coordinates where remarkable simplifications occur and allow for exact…
We prove that the area of cross-sections of light-cones, in space-times satisfying suitable energy conditions, is smaller than or equal to that of the corresponding cross-sections in Minkowski, or de Sitter, or anti-de Sitter space-time.…