Related papers: Generalizing Optical Geometry
Gravity whose nature is fundamental to the understanding of solar system, galaxies and the structure and evolution of the Universe, is theorized by the assumption of curved spacetime, according to Einstein`s general theory of relativity…
It is widely accepted that the fundamental geometrical law of nature should follow from an action principle. The particular subset of transformations of a system's dynamical variables that maintain the form of the action principle comprises…
Traditional geometry employs idealized concepts like that of a point or a curve, the operational definition of which relies on the availability of classical point particles as probes. Real, physical objects are quantum in nature though,…
To incorporate quantum nonlocality into general relativity, we propose that the preparation and measurement of a quantum system are simultaneous events. To make progress in realizing this proposal, we introduce a spacetime geometry that is…
General relativity can be presented in terms of other geometries besides Riemannian. In particular, teleparallel geometry (i.e., curvature vanishes) has some advantages, especially concerning energy-momentum localization and its…
This paper defines the spacetime geometry attached with observor as vacuum geometry (it defines the idea physical measurement geometry) and the spacetime geometry attached with matter as spacetime geometry. The initial spacetime geometry…
Quantum gravity phenomenology suggests an effective modification of the general relativistic dispersion relation of freely falling point particles caused by an underlying theory of quantum gravity. Here we analyse the consequences of…
A family of explicit exact solutions of Einstein's equations in four and higher dimensions is studied which describes photon rockets accelerating due to an anisotropic emission of photons. It is possible to prescribe an arbitrary motion, so…
We consider homogeneous and isotropic cosmological models in the framework of three geometrical theories of gravitation: in the Einstein general relativity they are given in terms of the curvature of the Levi-Civita connection in torsion…
General relativity uses curved space-time to describe accelerating frames. The movement of particles in different curved space-times can be regarded as equivalent physical processes based on the covariant transformation between different…
We explore, in the general relativistic context, the properties of the recently introduced GPS coordinates, as well as those of the associated frames and coframes. We show that they are covariant, and completely independent of any observer.…
When dealing with highly accurate modeling of time and frequency transfers into arbitrarily moving dielectrics medium, it may be convenient to work with Gordon's optical spacetime metric rather than the usual physical spacetime metric.…
We present a framework that reformulates gravitational lensing as an optical phenomenon governed by an effective refractive index, enabling exploration of modified gravity theories using undergraduate-level mathematics and optics. After…
The geodesic deviation equation (GDE) describes the tendency of objects to accelerate towards or away from each other due to spacetime curvature. The GDE assumes that nearby geodesics have a small rate of separation, which is formally…
The detection of gravitational waves (GWs) propagating through cosmic structures can provide invaluable information on the geometry and content of our Universe, as well as on the fundamental theory of gravity. In order to test possible…
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,…
Based on the Generalized Principle of Inertia, which states that: \emph{An inanimate object moves freely, that is, with zero acceleration, in its own spacetime, whose geometry is determined by all of the forces affecting it,} we geometrize…
We consider several aspects of the generalized multi-plane gravitational lens theory, in which light rays from a distant source are affected by several main deflectors, and in addition by the tidal gravitational field of the large-scale…
In this essay, we wish to propose a general principle: \it{the equation of motion or dynamics of a fundamental force should not be prescribed but instead be entirely driven by geometry of the appropriate spacetime manifold, and the equation…
Non-Euclidean method of the generalized geometry construction is considered. According to this approach any generalized geometry is obtained as a result of deformation of the proper Euclidean geometry. The method may be applied for…