Related papers: Penrose-Carter diagram for an uniformly accelerate…

We extend de la Fuente and Romero's defining equation for uniform acceleration in a general curved spacetime from linear acceleration to the full Lorentz covariant uniform acceleration. In a flat spacetime background, we have explicit…

The uniformly accelerated reference frame described by Hamilton, Desloge and Philpott involves the observers who perform the hyperbolic motion with constant proper acceleration gi. They start to move from different distances measured from…

We mathematically construct focal lenses for positive-mass particles in Minkowski space. Particles emanating from a point source, refocus with synchronized proper time regardless of initial direction and velocity. Minkowski space offers a…

Following a previous idea, a curved geometry is proposed as being valid in accelerated systems, in Minkowski space. The curvature turns out to be generated by the source of the accelerated motion. An exponential factor depending on $\rho$…

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…

It is widely thought that the quantum theory of de Sitter space requires the existence of a physical observer in the static patch. What exactly is meant by an observer is unclear; it could be anything from a few photons with energy just…

The Poincar\'e sector of a recently deformed conformal algebra is proposed to describe, after the identification of the deformation parameter with the Planck length, the symmetries of a new relativistic theory with two observer-independent…

A free hermitian conformal field theory is considered in Minkowski, de Sitter and anti-de Sitter spacetimes. The first part of the paper studies spacetime inversion and conformal inversion, wherein their role in the field quantization is…

This relativistic, time-travel spacetime is everywhere metrically flat, excepting a conical singularity. Observers following timelike geodesics can eventually encounter their past selves, aging in the opposite time sense. The spacetime is…

Consider an asymptotically Euclidean initial data set with a smooth marginally trapped surface (possibly a union of future and past multi-connected components) as inner boundary. By a further development of the spinorial framework…

Mathematical theory of an observer is elaborated upon the basis of A.Poincare's ideas on the nature of geometry and the role of observer's perceptive space. The said theory is generalizing reference frames theory in GR. Physical structure…

Classical geometry of de Sitter spacetime is reviewed in arbitrary dimensions. Topics include coordinate systems, geodesic motions, and Penrose diagrams with detailed calculations.

We briefly review two recently developed extensions of the Lorentzian geometry of spacetime and prove that they are in fact closely related. The first is the concept of observer space, which generalizes the space of Lorentzian observers,…

We construct a smooth trajectory in Minkowski spacetime that is inertial in the asymptotic past and future but undergoes approximately uniform acceleration for a finite duration. In a suitable limit, this trajectory reduces to the standard…

This paper gives a representation of the most general positive operator valued measure in Minkowski space-time, covariant with respect to the Poincare' group. It provides the correct mathematical description of the space-time coordinates of…

I demonstrate that the chart based approach to the study of the global structure of Lorentzian manifolds induces a homeomorphism of the manifold into a topological space as an open dense set. The topological boundary of this homeomorphism…

It is proposed four dimensional curved space-time with de-Sitter group of motion. Theory contain free dimension constants of length, impulse and action. Under infinite values of these parameters theory pass to usual Minkowski space-time…

This paper addresses the robustness of a prescribed-time observer for a class of nonlinear systems in the presence of disturbances and unmodeled dynamics. It is proven and demonstrated through simulations that the proposed observer…

After a review of the 1+3 point of view on non-inertial observers and of the problems of rotating reference frames, we underline that was is lacking in their treatment is a good global notion of simultaneity due to the restricted validity…

We study accelerating relativistic reference frames in Minkowski space-time under the harmonic gauge. It is well-known that the harmonic gauge imposes constraints on the components of the metric tensor and also on the functional form of…