Related papers: Special Relativity, Einstein Velocity Addition, an…
Recent advances, including gravitational wave detections and imaging of black hole shadows, have strongly validated general relativity. Nevertheless, ongoing cosmological observations suggest potential limitations of general relativity,…
We give precise details to support that observations of gravitational lensing at scales of individual, groups and clusters of galaxies can be understood in terms of non-Newtonian gravitational interactions with a relativistic structure…
This paper presents a brief but comprehensive introduction to certain mathematical techniques in General Relativity. Familiar mathematical procedures are investigated taking into account the complications of introducing a non trivial…
Following an approach proposed by Rosser for deriving the transformation equations of volume charge density and current density we derive the transformation equations for the space-time coordinates of the same event, for the mass and the…
The space of $n$-dimensional relativistic velocities normalized to $c = 1$, $$\mathbb{B} = \{\mathbf{v}\in\mathbb{R}^n\colon \|\mathbf{v}\| < 1\},$$ is naturally associated with Einstein velocity addition $\oplus_E$, which induces the…
In this extended note a critical discussion of an extension of the Lorentz transformations for velocities faster than the speed of light given recently by Hill and Cox is provided. The presented approach reveals the connection between…
We discuss pedagogical problems associated with the conventional approach in teaching relativity and the potential value of "Lorentzian route to relativity" for addressing these pedagogical problems. We think that Lorentzian approach may be…
This paper, which is meant to be a tribute to Minkowski's geometrical insight, rests on the idea that the basic observed symmetries of spacetime homogeneity and of isotropy of space, which are displayed by the spacetime manifold in the…
This article reviews the concept of Lorentz invariant relative velocity that is often misunderstood or unknown in high energy physics literature. The properties of the relative velocity allow to formulate the invariant flux and cross…
We recall the Einstein velocity addition on the open unit ball $\B$ of $\R^{3}$ and its algebraic structure, called the Einstein gyrogroup. We establish an isomorphism between the Einstein gyrogroup on $\B$ and the set of all qubit density…
This paper aims to provide physics teachers with tools to help deepen the understanding of the laws of electromagnetism. The fundamental contributions of our proposal are: a) to use quotes from mythical characters in the history of science…
A thought experiment first proposed by Sartori is analysed using the parallel velocity addition formula of special relativity. The distances and proper-time intervals between some similarly defined spatial coincidence events are found to be…
We summarize the main ideas of General Relativity and Lorentzian geometry, leading to a proof of the simplest of the celebrated Hawking-Penrose singularity theorems. The reader is assumed to be familiar with Riemannian geometry and point…
We are proving that the Lorentz boost entails the relative velocity to be ternary: ternary relative velocity is a velocity of a body with respect to an interior observer as seen by a preferred exterior-observer. The Lorentz boosts imply…
In this thesis we consider several aspects of general relativity relating to exact solutions of the Einstein equations. In the first part gravitational plane waves in the Rosen form are investigated, and we develop a formalism for writing…
Owing to the existence of an invariant length at the Planck scale, Einstein special relativity breaks down at that scale. A possible solution to this problem is arguably to replace the Poincar\'e invariant Einstein special relativity by a…
We revisit the problem of the Lorentz transformation of time-intervals in special relativity. We base our discussion on the time-interval transformation formula $ c\Delta t' = \gamma (c\Delta t - \vec{\beta} \cdot \Delta \vec{r}) $ in which…
This Resource Letter provides some guidance on issues that arise in teaching general relativity at both the undergraduate and graduate levels. Particular emphasis is placed on strategies for presenting the mathematical material needed for…
In this pedagogical article, we explore a powerful language for describing the notion of spacetime and particle dynamics intrinsic to a given fundamental physical theory, focusing on special relativity and its Newtonian limit. The starting…
Special relativity is reformulated as a symmetry property of space-time: Space-Time Exchange Invariance. The additional hypothesis of spatial homogeneity is then sufficient to derive the Lorentz transformation without reference to the…