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Pairs of metrics in a two-dimensional linear vector space are considered, one of which is a Minkowski type metric. Their simultaneous diagonalizability is studied and canonical presentations for them are suggested.

Lattice coverings in the real plane by Minkowski balls are studied. We exploit the duality of admissible lattices of Minkowski balls and inscribed convex symmetric hexagons of these balls. An explicit moduli space of the areas of these…

An algebraic characterization of vacuum states in Minkowski space is given which relies on recently proposed conditions of geometric modular action and modular stability for algebras of observables associated with wedge-shaped regions. In…

The motion of charged particles in spacetimes containing a submanifold of constant positive or negative curvature is considered, with the electromagnetic tensor proportional to the volume two-form form of the submanifold. In the positive…

We motivate and construct a mathematical theory for the separation of space and time in general relativity. The formalism only requires a single observer and an optional choice of reference frame at each instant. As the splitting is done…

Some standard definitions and results concerning foliations of dimension one and codimension one are introduced. A proper time foliation of Minkowski space is defined and contrasted with the foliation that is defined by the time coordinate.…

A world sheet in Lorentz-Minkowski space is a timelike submanifold consisting of a one-parameter family of spacelike submanifolds in Lorentz-Minkowski space. In this paper we investigate differential geometry of world sheets in…

The complex time WKB (CWKB) approximation has been an effective technique to understand particle production in curved as well as in flat spacetime. Earlier we obtained the standard results on particle production in time dependent gauge in…

The concept of an observer and their associated rest space is defined in a pre-metric (i.e., projective-geometric) context that relates to time+space decompositions of the tangent bundle to space-time. The transformation from one observer…

We construct a positive constant curvature space by identifying some points along a Killing vector in a de Sitter Space. This space is the counterpart of the three-dimensional Schwarzschild-de Sitter solution in higher dimensions. This…

A generalised equivalence principle is put forward according to which space-time symmetries and internal quantum symmetries are indistinguishable before symmetry breaking. Based on this principle, a higher-dimensional extension of Minkowski…

In a queueing system involving multiple service windows, choice behavior is a significant concern. This paper incorporates the choice of service windows into a queueing model with a floor represented by discrete cells. We contrived a…

Massive Klein-Gordon theory is quantized on a timelike hyperplane in Minkowski space using the framework of general boundary quantum field theory. In contrast to previous work, not only the propagating sector of the phase space is…

An extended object is considered on the Minkowski background in the form of a space-time bag, which is bounded by a certain surface confining an internal substance. An internal metric is built starting from the symmetry principles rather…

We investigate scaling and correlations of the energy and momentum in an evolving network of cosmic strings in Minkowski space. These quantities are of great interest, as they must be understood before accurate predictions for the power…

Quantum operators of coordinates and momentum components of a particle in the Minkowski spacetime can belong to the generalized Snyder-Yang algebra and produce a quantum phase space with three new constants in the general case. With account…

In 1908, Minkowski put forward the idea that invariance under what we call today the Lorentz group, $GL(1,3, {\bf R})$, would be more meaningful in a four-dimensional space-time continuum. This suggestion implies that space and time are…

A subset of a metric space is a k-distance set if there are exactly k non-zero distances occuring between points. We conjecture that a k-distance set in a d-dimensional Banach space (or Minkowski space), contains at most (k+1)^d points,…

In a (1+1)-dimensional midi-superspace model for gravitational plane waves, a flat space-time condition is imposed with constraints derived from null Killing vectors. Solutions to a straightforward regularization of these constraints have…

We propose a method of projecting the quantum states from a state space of a given geometry into another state space generated by a different geometry, taking care on the correct normalization which is crucial in interpreting the quantum…