36 research outputs found
Ricci flow for homogeneous compact models of the universe
Using quaternions, we give a concise derivation of the Ricci tensor for
homogeneous spaces with topology of the 3-dimensional sphere. We derive
explicit and numerical solutions for the Ricci flow PDE and discuss their
properties. In the collapse (or expansion) of these models, the interplay of
the various components of the Ricci tensor are studied. We dedicate this paper
to honor the work of Josh Goldberg.Comment: 18 pages, 2 figure
Pressure as a Source of Gravity
The active mass density in Einstein's theory of gravitation in the analog of
Poisson's equation in a local inertial system is proportional to .
Here is the density of energy and its pressure for a perfect fluid.
By using exact solutions of Einstein's field equations in the static case we
study whether the pressure term contributes towards the mass
Interacting Constituents in Cosmology
Universe evolution, as described by Friedmann's equations, is determined by
source terms fixed by the choice of pressure energy-density equations
of state . The usual approach in Cosmology considers equations of
state accounting only for kinematic terms, ignoring the contribution from the
interactions between the particles constituting the source fluid. In this work
the importance of these neglected terms is emphasized. A systematic method,
based on the Statistical Mechanics of real fluids, is proposed to include them.
A toy-model is presented which shows how such interaction terms can engender
significant cosmological effects.Comment: 24 pages, 6 figures. It includes results presented in "Cosmic
Acceleration from Elementary Interactions" [arXiv:gr-qc/0512135]. Citations
added in v.
Shear free solutions in General Relativity Theory
The Goldberg-Sachs theorem is an exact result on shear-free null geodesics in
a vacuum spacetime. It is compared and contrasted with an exact result for
pressure-free matter: shear-free flows cannot both expand and rotate. In both
cases, the shear-free condition restricts the way distant matter can influence
the local gravitational field. This leads to intriguing discontinuities in the
relation of the General Relativity solutions to Newtonian solutions in the
timelike case, and of the full theory to the linearised theory in the null
case.
It is a pleasure to dedicate this paper to Josh Goldberg.Comment: 17 pages, no figures. For GRG special issue in honor of Josh Goldber
Theorems on shear-free perfect fluids with their Newtonian analogues
In this paper we provide fully covariant proofs of some theorems on
shear-free perfect fluids. In particular, we explicitly show that any
shear-free perfect fluid with the acceleration proportional to the vorticity
vector (including the simpler case of vanishing acceleration) must be either
non-expanding or non-rotating. We also show that these results are not
necessarily true in the Newtonian case, and present an explicit comparison of
shear-free dust in Newtonian and relativistic theories in order to see where
and why the differences appear.Comment: 23 pages, LaTeX. Submitted to GR
Effect of inhomogeneity of the Universe on a gravitationally bound local system: A no-go result for explaining the secular increase in the astronomical unit
We will investigate the influence of the inhomogeneity of the universe,
especially that of the Lema{\^i}tre-Tolman-Bondi (LTB) model, on a
gravitationally bound local system such as the solar system. We concentrate on
the dynamical perturbation to the planetary motion and derive the leading order
effect generated from the LTB model. It will be shown that there appear not
only a well-known cosmological effect arisen from the homogeneous and isotropic
model, such as the Robertson-Walker (RW) model, but also the additional terms
due to the radial inhomogeneity of the LTB model. We will also apply the
obtained results to the problem of secular increase in the astronomical unit,
reported by Krasinsky and Brumberg (2004), and imply that the inhomogeneity of
the universe cannot have a significant effect for explaining the observed
.Comment: 12 pages, no figure, accepted for publication in Journal of
Astrophysics and Astronom
Gravitational-wave research as an emerging field in the Max Planck Society. The long roots of GEO600 and of the Albert Einstein Institute
On the occasion of the 50th anniversary since the beginning of the search for
gravitational waves at the Max Planck Society, and in coincidence with the 25th
anniversary of the foundation of the Albert Einstein Institute, we explore the
interplay between the renaissance of general relativity and the advent of
relativistic astrophysics following the German early involvement in
gravitational-wave research, to the point when gravitational-wave detection
became established by the appearance of full-scale detectors and international
collaborations. On the background of the spectacular astrophysical discoveries
of the 1960s and the growing role of relativistic astrophysics, Ludwig Biermann
and his collaborators at the Max Planck Institute for Astrophysics in Munich
became deeply involved in research related to such new horizons. At the end of
the 1960s, Joseph Weber's announcements claiming detection of gravitational
waves sparked the decisive entry of this group into the field, in parallel with
the appointment of the renowned relativist Juergen Ehlers. The Munich area
group of Max Planck institutes provided the fertile ground for acquiring a
leading position in the 1970s, facilitating the experimental transition from
resonant bars towards laser interferometry and its innovation at increasingly
large scales, eventually moving to a dedicated site in Hannover in the early
1990s. The Hannover group emphasized perfecting experimental systems at pilot
scales, and never developed a full-sized detector, rather joining the LIGO
Scientific Collaboration at the end of the century. In parallel, the Max Planck
Institute for Gravitational Physics (Albert Einstein Institute) had been
founded in Potsdam, and both sites, in Hannover and Potsdam, became a unified
entity in the early 2000s and were central contributors to the first detection
of gravitational waves in 2015.Comment: 94 pages. Enlarged version including new results from further
archival research. A previous version appears as a chapter in the volume The
Renaissance of General Relativity in Context, edited by A. Blum, R. Lalli and
J. Renn (Boston: Birkhauser, 2020
Making Public the Private Life of Plants: The contribution of informal learning environments
Conservation of energy-momentum of matter as the basis for the gauge theory of gravitation
According to Yang \& Mills (1954), a {\it conserved} current and a related
rigid (`global') symmetry lie at the foundations of gauge theory. When the
rigid symmetry is extended to a {\it local} one, a so-called gauge symmetry, a
new interaction emerges as gauge potential ; its field strength is . In gravity, the conservation of the energy-momentum current of
matter and the rigid translation symmetry in the Minkowski space of special
relativity lie at the foundations of a gravitational gauge theory. If the
translation invariance is made local, a gravitational potential
arises together with its field strength . Thereby
the Minkowski space deforms into a Weitzenb\"ock space with nonvanishing
torsion but vanishing curvature. The corresponding theory is reviewed and
its equivalence to general relativity pointed out. Since translations form a
subgroup of the Poincar\'e group, the group of motion of special relativity,
one ought to straightforwardly extend the gauging of the translations to the
gauging of full Poincar\'e group thereby also including the conservation law of
the {\it angular momentum} current. The emerging Poincar\'e gauge (theory of)
gravity, starting from the viable Einstein-Cartan theory of 1961, will be
shortly reviewed and its prospects for further developments assessed.Comment: 46 pages, 4 figures, minor corrections, references added,
contribution to "One Hundred Years of Gauge Theory" edited by S. De Bianchi
and C. Kiefe