Related papers: Strains in General Relativity
A geometric theory for spacetimes whose world lines associated with physical particles have an upper bound for the proper acceleration is developed. After some fundamental remarks on the requirements that the classical dynamics for point…
In the framework of the theory of scale relativity, we suggest a solution to the cosmological problem of the formation and evolution of gravitational structures on many scales. This approach is based on the giving up of the hypothesis of…
A geometrical pattern is a set of points with all pairwise distances (or, more generally, relative distances) specified. Finding matches to such patterns has applications to spatial data in seismic, astronomical, and transportation…
We investigate the possibility of extending Newton's second law to the general framework of theories in which special relativity is locally valid, and in which gravitation changes the flat Galilean space-time metric into a curved metric.…
We show that the concept of total variance of a spin state, defined as the average of the variances of spin projection measurements along three orthogonal axes, also gives the rotational speed of the state in projective space, averaged over…
We advance an universal approach to the construction of kinematics in non-inertial and, in particular, rotating reference frames. On its basis a 10-dimensional space including three projections of velocity vector and three turn angles in…
Relativity is an integral part of positioning systems, and this is taken into account in today's practice by applying many "relativistic corrections" to computations performed using concepts borrowed from Galilean physics. A different,…
Multiple images, giant arcs, Einstein cross, fold, cusp, lip, caustics, critical lines, sources, mapping, time delay, arclets, weak shear, magnification bias, depletion, ellipticities, polarization, smearing, convergence, kernel, mass…
The concept of a physical space, which actualizes Euclidean geometry, is not confined to the statics of solids but extensible to the phenomena where Newtonian mechanics is valid, defining its concept of time. The laws of propagation of…
The curvature invariants have been subject of interest due to the debate concerning the notions of intrinsic/extrinsic frame-dragging, the use of the electromagnetic analogy in such classification, and the question of whether there is a…
We define a new parameter `cumulative drag index' for a particle in circular orbit in a stationary, axisymmetric gravitational field and study its behaviour in the two well known solutions of general relativity {\it viz.}, the Kerr…
Three theoretical criteria for gravitational theories beyond general relativity are considered: obtaining the cosmological constant as an integration constant, deriving the energy conservation law as a consequence of the field equations,…
We construct a theory of particles moving in curved both momentum space and spacetime, being a generalization of Relative Locality. We find that in order to construct such theory, with desired symmetries, including the general coordinate…
Propagation of relativistic particles in the Schwarzschild gravitational field is studied. Particles emitted radially outward with speed at infinity exceeding c/2^0.5 are observed to be accelerated in the gravitational field by a distant…
Concepts like peculiar velocity, gravitational force, and power spectrum and their interrelationships are of utmost importance in the theories of structure formation. The observational implementation of these concepts is usually based on…
Motion of test particles along rotating curved trajectories is considered. The problem is studied both in the laboratory and the rotating frames of reference. It is assumed that the system rotates with the constant angular velocity $\omega…
Understanding the deflection of light by a massive deflector, as well as the associated gravitational lens phenomena, require the use of the theory of General Relativity. I consider here a classical approach, based on Newton's equation of…
We address a subject that could have been analyzed century ago: how does the universe of general relativity look like when it would have been filled with solid matter? Solids break spontaneously the translations and rotations of space…
The possible relation of the wave nature of particles to gravitation as an emergent phenomenon is addressed. Hypothetical particles are considered as spatially confined oscillations (SCOs) and are constructed through the superposition of…
Observations of compact objects in the electromagnetic spectrum and the detection of gravitational waves from them can lead to quantitative tests of the theory of general relativity in the strong-field regime following two very different…