Related papers: Relativistic rigid systems and the cosmic expansio…
We study the acceleration and collisions of rigid bodies in special relativity. After a brief historical review, we give a physical definition of the term `rigid body' in relativistic straight line motion. We show that the definition of…
This paper challenges some of the common assumptions underlying the mathematics used to describe the physical world. We start by reviewing many of the assumptions underlying the concepts of real, physical, rigid bodies and the translational…
Cosmological observations are beginning to reach a level of precision that allow us to test some of the most fundamental assumptions in our working model of the Universe. One such an assumption is that gravity is governed by the General…
In this contribution I wish to address the question whether, and how, the global cosmological expansion influences local physics. I argue that a pseudo Newtonian picture can be quite accurate if "expansion" is taken to be an attribute of…
The current standard cosmological model is constructed within the framework of general relativity with a cosmological constant $\Lambda$, which is often associated with dark energy, and phenomenologically explains the accelerated cosmic…
The notion of a rigid quasilocal frame (RQF) provides a geometrically natural way to define a system in general relativity, and a new way to analyze the problem of motion. An RQF is defined as a two-parameter family of timelike worldlines…
The discovery that the Universe is accelerating in its expansion has brought the basic concept of cosmic expansion into question. An analysis of the evolution of this concept suggests that the paradigm that was finally settled into prior to…
We show the rigid singularity theorem, that is, a globally hyperbolic spacetime satisfying the strong energy condition and containing past trapped sets, either is timelike geodesically incomplete or splits isometrically as space $\times$…
The interplay between cosmological expansion and local attraction in a gravitationally bound system is revisited in various regimes. First, weakly gravitating Newtonian systems are considered, followed by various exact solutions describing…
In this paper I argue for a reassessment of special relativity. The fundamental theory of relativity applicable in this Universe has to be consistent with the existence of the massive Universe, and with the effects of its gravitational…
This is the first in a series of papers devoted to fully general-relativistic $N$-body simulations applied to late-time cosmology. The purpose of this paper is to present the combination of a numerical relativity scheme, discretization…
In this thesis the cosmological constant is investigated from two points of view. First, we study the influence of a time-dependent cosmological constant on the late-time expansion of the universe. Thereby, we consider several combinations…
In the standard approach to studying cosmological structure formation, the overall expansion of the Universe is assumed to be homogeneous, with the gravitational effect of inhomogeneities encoded entirely in a Newtonian potential. A topic…
While modern cosmology, founded in the language of general relativity, is almost a century old, the meaning of the expansion of space is still being debated. In this paper, the question of radar ranging in an expanding universe is examined,…
Both from gravitational (G) experiments and from a new theoretical approach based on a particle model it is proved that the classical invariability of the bodies, after a change of relative rest-position with respect to other bodies, it is…
Numerical N-body simulations of large scale structure formation in the universe are based on Newtonian gravity. However, according to our current understanding, the most correct theory of gravity is general relativity. It is therefore…
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,…
The analysis of axisymmetric spacetimes, dynamical or stationary, is usually made in the reduced space. We prove here a stability property of the quo- tient space and use it together with minimal surface techniques to constraint the shape…
The paper shows how a generalization of the elasticity theory to four dimensions and to space-time allows for a consistent description of the homogeneous and isotropic universe, including the accelerated expansion. The analogy is manifested…
The absence of an identified consequence at solar system scale of the cosmological space expansion is usually explained considering that space expansion does not affect local anysotropies in matter distribution. This can also be explained…