Related papers: Explicit solutions for relativistic acceleration a…
We show that starting with the addition law of parallel speeds derived as a consequence of the invariance of the speed of light, the Lorentz transformations for the space-time coordinates can be derived.
Special relativity corresponds to hyperbolic geometry at constant velocity while the so-called general relativity corresponds to hyperbolic geometry of uniformly accelerated systems. Generalized expressions for angular momentum, centrifugal…
Classical relativistic system of point particles coupled with an electromagnetic field is considered in the three-dimensional representation. The gauge freedom connected with the chronometrical invariance of the four-dimensional description…
Beside diffeomorphism invariance also manifest SO(3,1) local Lorentz invariance is implemented in a formulation of Einstein Gravity (with or without cosmological term) in terms of initially completely independent vielbein and spin…
We consider the Euler equations governing relativistic compressible fluids evolving in the Minkowski spacetime with several spatial variables. We propose a new symmetrization which makes sense for solutions containing vacuum states and, for…
The relativistic acceleration of an electron in a uniform gravitational field is calculated numerically using the generalization of the Dirac equation to curved spacetime. Equivalent results are also obtained analytically using an iterative…
There are many different formulations of relativistic elasticity. Most of them are only concerned with formal questions rather than questions regarding the PDE point of view. The aim of this thesis is to obtain various local existence…
Homogeneity of space and time, spatial isotropy, principle of relativity and the existence of a finite speed limit (or its variants) are commonly believed to be the only axioms required for developing the special theory of relativity…
We introduce observables associated with the space-time position of a quantum point defined by the intersection of two light pulses. The time observable is canonically conjugated to the energy. Conformal symmetry of massless quantum fields…
A new term describing interactions between charge and potentials may be added to the right hand side of the Einstein equations. In the proposed term an additional tensor has been introduced containing a charge density, analogous to the…
The present work shows that through a suitable change of variables relativistic dynamics can be mapped to light propagation in a non-homogeneous medium. A particle's trajectory through the modified space-time is thus formally equivalent to…
We study the relativistic Euler equations on the Minkowski spacetime background. We make assumptions on the equation of state and the initial data that are relativistic analogs of the well-known physical vacuum boundary condition, which has…
The classical and quantum dynamics of simple time-reparametrization- invariant models containing two degrees of freedom are studied in detail. Elimination of one ``clock'' variable through the Hamiltonian constraint leads to a description…
Einstein's relativity theory demands that all meaningful physical objects should be defined covariantly, i.e. in a coordinate independent way. Concepts of relative velocity, acceleration, gravity acceleration and gravity potential are…
We have defined slowness (or reciprocal velocity) corresponding to v as cc/v, where c is the speed of light and v is the corresponding velocity. Velocity and slowness are images of each other. Reciprocal symmetric law of addition of…
The starting point of the theory of Special Relativity$^1$ is the Lorentz transformation, which in essence describes the lack of absolute measurements of space and time. These effects came about when one applies the Second Relativity…
We study the Lie symmetries of non-relativistic and relativistic higher order constant motions, in $d$ spatial dimensions, like constant acceleration, constant rate-of-change -of-acceleration (constant jerk), and so on. In the…
Cylindrical spacetimes with rotation are studied using the Newmann-Penrose formulas. By studying null geodesic deviations the physical meaning of each component of the Riemann tensor is given. These spacetimes are further extended to…
We develop quantum electrodynamics into a kinetic-theory-like evolution equation for electrons, positrons and photons. To keep the "collision rules" simple, we make use of longitudinal and temporal photons in addition to the usual…
Minkowski spacetime is a convenient setting for the study of the relativistic dynamics of particles and fields in the vacuum. In order to study events that occur in a dielectric or other linear medium, we adopt the familiar continuum…