Related papers: Fermi coordinates, simultaneity, and expanding spa…
Our aim in this paper is two-fold. We establish a novel geometric characterization of the Roberson-Walker (RW) spacetime and, along the process, we find a canonical form of the RW metric associated to an arbitrary timelike curve and an…
We find exact Fermi coordinates for timelike geodesic observers for a class of spacetimes that includes anti-de Sitter spacetime, de Sitter spacetime, the constant density interior Schwarzschild spacetime with positive, zero, and negative…
In metric-affine gravity, both the gravitational and matter actions depend not just on the metric, but also on the independent affine connection. Thus matter can be modeled as a hyperfluid, characterized by both the energy-momentum and…
We examine the solution of the constraints in spherically symmetric general relativity when spacetime has a flat spatial hypersurface. We demonstrate explicitly that given one flat slice, a foliation by flat slices can be consistently…
In this work we study the geometric properties of spacelike foliations by hypersurfaces on a Lorentz manifold. We find an equation that relates the foliation with the ambient manifold and apply it to investigate conditions for the leaves…
The extension of the so-called "empty" (with gravity and antigravity that compensate each other in full or do not exist at all) universe and cosmological redshift in it are considered in this paper. Its flat space-time can be submitted not…
In an attempt to generalize general relativity, we propose a new Hermitian theory of gravity. Space-time is generalized to space-time-momentum-energy and both the principles of general covariance and equivalence are extended. The theory is…
It is shown that the Fermi-Walker gauge allows the general solution of determining the metric given the sources, in terms of simple quadratures. We treat the general stationary problem providing explicit solving formulas for the metric and…
Fermi coordinates are directly constructed in de Sitter and Goedel spacetimes and the corresponding exact coordinate transformations are given explicitly. The quasi-inertial Fermi coordinates are then employed to discuss the dynamics of a…
It has been demonstrated that a modern stage of the Universe expansion may be described in accordance with the observations within the scope of the space-time conformal geometry. The clock synchronization procedure in SR has been…
With the aid of a Fermi-Walker chart associated with an orthonormal frame attached to a time-like curve in spacetime, a discussion is given of relativistic balance laws that may be used to construct models of massive particles with spin,…
We develop the spacetime approach to gravitational lensing by spherically symmetric perturbations of flat, cosmological constant-dominated Friedman-Robertson-Walker metrics. The geodesics of the spacetime are expressed as integral…
Context. Explaining the accelerated expansion of the Universe is one of the fundamental challenges in physics today. Cosmography provides information about the evolution of the universe derived from measured distances, assuming only that…
We consider universes that are close to Friedmann-Robertson-Walker in the sense that metric perturbations, their time derivatives and first spatial derivatives are small, but second spatial derivatives are not constrained. We show that if…
A characterization of the foliation by spacelike slices of an $(n+1)$-dimensional spatially closed Generalized Robertson-Walker spacetime is given by means of studying a natural mean curvature type equation on spacelike graphs. Under some…
The generic acceleration model for ultra high energy cosmic rays, which has been introduced in {\tt 1006.5708 [astro-ph.HE]}, suggests various types of electromagnetic interactions between cosmic charged particles and the different types of…
For a given space-time and for an arbitrary time-like geodesic, we analyze the conditions for the construction of Fermi coordinates so that they are also rigid covariant. We then apply these conditions to linear plane gravitational waves.
We examine in the context of general relativity the dynamics of a spatially flat Robertson-Walker universe filled with a classical minimally coupled scalar field \phi of exponential potential ~ e^{-\mu\phi} plus pressureless baryonic…
The starting point of this work is the principle that all movement of particles and photons in the observable Universe must follow geodesics of a 4-dimensional space where time intervals are always a measure of geodesic arc lengths, i.e.…
How do we appropriately fit a model based on an idealised Friedmann-Lema\^{}tre Robertson-Walker spacetime to observations made from a single location in a lumpy Universe? We address this question for surveys that measure the imprints of…