8 research outputs found
A river model of space
Within the theory of general relativity gravitational phenomena are usually
attributed to the curvature of four-dimensional spacetime. In this context we
are often confronted with the question of how the concept of ordinary physical
three-dimensional space fits into this picture. In this work we present a
simple and intuitive model of space for both the Schwarzschild spacetime and
the de Sitter spacetime in which physical space is defined as a specified set
of freely moving reference particles. Using a combination of orthonormal basis
fields and the usual formalism in a coordinate basis we calculate the physical
velocity field of these reference particles. Thus we obtain a vivid description
of space in which space behaves like a river flowing radially toward the
singularity in the Schwarzschild spacetime and radially toward infinity in the
de Sitter spacetime. We also consider the effect of the river of space upon
light rays and material particles and show that the river model of space
provides an intuitive explanation for the behavior of light and particles at
and beyond the event horizons associated with these spacetimes.Comment: 22 pages, 5 figure
Focusing of geodesic congruences in an accelerated expanding Universe
We study the accelerated expansion of the Universe through its consequences
on a congruence of geodesics. We make use of the Raychaudhuri equation which
describes the evolution of the expansion rate for a congruence of timelike or
null geodesics. In particular, we focus on the space-time geometry contribution
to this equation. By straightforward calculation from the metric of a
Robertson-Walker cosmological model, it follows that in an accelerated
expanding Universe the space-time contribution to the Raychaudhuri equation is
positive for the fundamental congruence, favoring a non-focusing of the
congruence of geodesics. However, the accelerated expansion of the present
Universe does not imply a tendency of the fundamental congruence to diverge. It
is shown that this is in fact the case for certain congruences of timelike
geodesics without vorticity. Therefore, the focusing of geodesics remains
feasible in an accelerated expanding Universe. Furthermore, a negative
contribution to the Raychaudhuri equation from space-time geometry which is
usually interpreted as the manifestation of the attractive character of gravity
is restored in an accelerated expanding Robertson-Walker space-time at high
speeds.Comment: 11 pages, 2 figures. Final version changed to match published version
in JCAP. References updated. Conclusions unchange
On the non-attractive character of gravity in f(R) theories
Raychaudhuri equation is found provided that particular energy conditions are assumed and regardless the considered solution of the Einstein's equations. This fact is usually interpreted as a manifestation of the attractive character of gravity. Nevertheless, a positive contribution to Raychaudhuri equation from space-time geometry should occur since this is the case in an accelerated expanding Robertson-Walker model for congruences followed by fundamental observers. Modified gravity theories provide the possibility of a positive contribution although the standard energy conditions are assumed. We address this important issue in the context of f(R) theories, deriving explicit upper bounds for the contribution of space-time geometry to the Raychaudhuri equation. Then, we examine the parameter constraints for some paradigmatic f(R) models in order to ensure a positive contribution to this equation. Furthermore, we consider the implications of these upper bounds in the equivalent formulation of f(R) theories as a Brans-Dicke model