Related papers: Einstein's mirror revisited
We give a derivation of the Einstein equation for gravity which employs a definition of the local energy density of the gravitational field as a symmetric second rank tensor whose value for each observer gives the trace of the spatial part…
An interpretation of selected parts of Newton's Principia, with modern notation and methods. Keplers Laws are derived from an inverse square law using Newton's methods.
We discuss how the diffraction theory of a single translation bounded measure or a family of such measures can be understood within the framework of unitary group representations. This allows us to prove an orthogonality feature of measures…
We present an elementary, symmetry-first derivation of the Lorentz transformation together with a methodological clarification of the linearity step. Starting from the Principle of Relativity, supplemented by spacetime homogeneity,…
We provide an explicit geometric algorithm involving only ruler and compass constructions in order to specify the specular reflection point on the surface of a reflecting sphere of radius $r$ given two focal points $A$ and $B$ lying outside…
We study the general theorem about gravitational lensing which states the relationship between the numbers of images with different parities. Our formulation allows an extension to the nontransparent and singular model.
Here we give a more detailed account of the part of the conference report that was devoted to reinterpreting the Einstein `unified models of gravity and electromagnetism' (1923) as the unified theory of dark energy (cosmological constant)…
Many authors noted that the principle of relativity, together with space-time symmetries, suffices to derive Lorentz-like coordinate transformations between inertial frames. These contain a free parameter, $k$, (equal to $c^{-2}$ in special…
Evaluation of the additive constants in the space-time Lorentz transformation equations required, according to Einstein, to correctly describe synchronised clocks at different spatial locations, reveals the spurious and unphysical nature of…
In this paper we study the light bending caused by a slowly rotating source in the context of quadratic theories of gravity, in which the Einstein--Hilbert action is extended by additional terms quadratic in the curvature tensors. The…
Before we discuss the deflection of light in a gravitational field, we give a brief overview of some basic physical formulas on photon properties, generation and propagation. The much debated problems of the redshift and the photon…
An explicit form for the geodesic equations that would describe diffracted light rays is obtained and the Levi-Civita connection that enters into it is shown to be a sum of contributions from the metric of the ambient space, the index of…
I discuss the conformal approach to the numerical simulation of radiating isolated systems in general relativity. The method is based on conformal compactification and a reformulation of the Einstein equations in terms of rescaled…
There are many papers devoted to derivation of Lorentz Transformations (LT). Many people have pro posed alternative derivations. Their analysis allows looking at LT and their consequences from different standpoints. At the same time it is…
Electromagnetism in an inhomogeneous dielectric medium at rest is described using the methods of differential geometry. In contrast to a general relativistic approach the electromagnetic fields are discussed in three-dimensional space only.…
We study the renormalized volume of a conformally compact Einstein manifold. In even dimensions, we derive the analogue of the Chern-Gauss-Bonnet formula incorporating the renormalized volume. When the dimension is odd, we relate the…
General relativistic deflection of light by mass, dipole, and quadrupole moments of gravitational field of a moving massive planet in the Solar system is derived in the approximation of the linearized Einstein equations. All terms of order…
The Einstein theories of space-time and gravity as well the stander cosmology are reconstructed thoroughly in this paper based on flat reference frame. The rational parts of the Einstein theories are reserved while the irrational parts…
The application of numerical relativity to cosmological spacetimes is providing new insights into the behavior of Einstein's equations, beyond common approximations. In order for simulations to be performed as accurately and efficiently as…
The basic laws of geometrical optics can be deduced from energy-momentum conservation for electromagnetic waves, without other wave concepts. However, the concept of quanta is required; it arises naturally, hence such a hypothesis could…