Related papers: Observers with constant proper acceleration, const…

We compute analytically differential invariants for accelerating, rotating and charged black holes with a cosmological constant $\Lambda$. In particular, we compute in closed form novel explicit algebraic expressions for curvature…

All existing 4-coordinate systems centered on the world-line of an accelerated observer are only locally defined like it happens for Fermi coordinates both in special and general relativity. As a consequence, it is not known how…

I present a way to visualize the concept of curved spacetime. The result is a curved surface with local coordinate systems (Minkowski Systems) living on it, giving the local directions of space and time. Relative to these systems, special…

Minkowski famously introduced the concept of a space-time continuum in 1908, merging the three dimensions of space with an imaginary time dimension $ i c t $, with the unit imaginary producing the correct spacetime distance $ x^2 - c^2 t^2…

We argue that space-time properties are not absolute with respect to the used frame of reference as is to be expected according to ideas of relativity of space and time properties by Berkley - Leibnitz - Mach- Poincar\'{e}. From this point…

The characteristics of the memory of accelerated motion in Minkowski spacetime are discussed within the framework of the nonlocal theory of accelerated observers. Two types of memory are distinguished: kinetic and dynamic. We show that only…

In this paper, we give the definition of the natural mate of a non-null Frenet curve in Minkowski 3-spaces. The main purpose of this paper is to prove some relationships between a non-null Frenet curve and its natural mate. In particular,…

We use the isotropic projection of Laguerre geometry in order to establish a correspondence between plane curves and null curves in the Minkowski $3$-space. We describe the geometry of null curves (Cartan frame, pseudo-arc parameter,…

We present an introduction to the study of a relativistic particle moving under the influence of its own Frenet-Serret curvatures. With the aim of introducing the notation and conventions used in this paper, we first recall the action of a…

The four dimensional spacetime continuum, as first conceived by Minkowski, has become the dominant framework within which to describe physical laws. In this paper, we show how this four-dimensional structure is a natural property of…

Newton's Second Law defines inertial mass as the ratio of the applied force on an object to the responding acceleration of the object (viz., F=ma). Objects that exhibit finite accelerations under finite forces are described as being…

Using elementary knowledge of Special Relativity, we design a computational classroom experiment in excel and python. Here, we show that any inertial observer $\mathcal{B}$ with an arbitrary speed $u_\mathcal{B}$ is associated with a unique…

We propose a new classical theory of gravity which is based on the principle of equivalence and assumption that gravity, similarly to electrodynamics, is described by a vector field in Minkowski space-time. We show that such assumptions…

Assuming that an accelerated observer with four-velocity ${\bf u}_{\rm R}$ in a curved spacetime attributes the standard Bekenstein-Hawking entropy and Unruh temperature to his "local Rindler horizon", we show that the $\rm \it change$ in…

We consider a curve $\alpha=\alpha(s)$ in Minkowski 3-space $E_1^3$ and denote by $\{T,N,B}$ the Frenet frame of $\alpha$. We say that $\alpha$ is a slant helix if there exists a fixed direction $U$ of $E_1^3$ such that the function…

We consider a continuous-variable quantum teleportation protocol between a uniformly accelerated sender in the right Rindler wedge, a conformal receiver restricted to the future light cone, and an inertial observer in the Minkowski vacuum.…

Geodesic completeness is typically regarded as a basic criterion to determine whether a given spacetime is regular or singular. However, the principle of general covariance does not privilege any family of observers over the others and,…

This work deals with the questions of absolute space and relativity. In particular, an alternative derivation of the effects described by special relativity is provided, which is based on a description that assumes a privileged reference…

The perturbation theory expansion presented earlier to describe the phase-ordering kinetics in the case of a nonconserved scalar order parameter is generalized to the case of the $n$-vector model. At lowest order in this expansion, as in…

We provide a unified description of Heinz-type mean curvature estimates under an assumption on the gradient bound for space-like graphs and time-like graphs in the Lorentz-Minkowski space. As a corollary, we give a unified vanishing theorem…