24 research outputs found
The Confrontation between General Relativity and Experiment
The status of experimental tests of general relativity and of theoretical
frameworks for analysing them is reviewed. Einstein's equivalence principle
(EEP) is well supported by experiments such as the Eotvos experiment, tests of
special relativity, and the gravitational redshift experiment. Future tests of
EEP and of the inverse square law are searching for new interactions arising
from unification or quantum gravity. Tests of general relativity at the
post-Newtonian level have reached high precision, including the light
deflection, the Shapiro time delay, the perihelion advance of Mercury, and the
Nordtvedt effect in lunar motion. Gravitational-wave damping has been detected
in an amount that agrees with general relativity to better than half a percent
using the Hulse-Taylor binary pulsar, and other binary pulsar systems have
yielded other tests, especially of strong-field effects. When direct
observation of gravitational radiation from astrophysical sources begins, new
tests of general relativity will be possible.Comment: 89 pages, 8 figures; an update of the Living Review article
originally published in 2001; final published version incorporating referees'
suggestion
Exploring new physics frontiers through numerical relativity
The demand to obtain answers to highly complex problems within strong-field gravity has been met with significant progress in the numerical solution of Einstein's equations - along with some spectacular results - in various setups. We review techniques for solving Einstein's equations in generic spacetimes, focusing on fully nonlinear evolutions but also on how to benchmark those results with perturbative approaches. The results address problems in high-energy physics, holography, mathematical physics, fundamental physics, astrophysics and cosmology
Modern tests of Lorentz invariance
Motivated by ideas about quantum gravity, a tremendous amount of effort over
the past decade has gone into testing Lorentz invariance in various regimes.
This review summarizes both the theoretical frameworks for tests of Lorentz
invariance and experimental advances that have made new high precision tests
possible. The current constraints on Lorentz violating effects from both
terrestrial experiments and astrophysical observations are presented.Comment: Modified and expanded discussions of various points. Numerous
references added. Version matches that accepted by Living Reviews in
Relativit
Geometry and field theory in multi-fractional spacetime
We construct a theory of fields living on continuous geometries with
fractional Hausdorff and spectral dimensions, focussing on a flat background
analogous to Minkowski spacetime. After reviewing the properties of fractional
spaces with fixed dimension, presented in a companion paper, we generalize to a
multi-fractional scenario inspired by multi-fractal geometry, where the
dimension changes with the scale. This is related to the renormalization group
properties of fractional field theories, illustrated by the example of a scalar
field. Depending on the symmetries of the Lagrangian, one can define two
models. In one of them, the effective dimension flows from 2 in the ultraviolet
(UV) and geometry constrains the infrared limit to be four-dimensional. At the
UV critical value, the model is rendered power-counting renormalizable.
However, this is not the most fundamental regime. Compelling arguments of
fractal geometry require an extension of the fractional action measure to
complex order. In doing so, we obtain a hierarchy of scales characterizing
different geometric regimes. At very small scales, discrete symmetries emerge
and the notion of a continuous spacetime begins to blur, until one reaches a
fundamental scale and an ultra-microscopic fractal structure. This fine
hierarchy of geometries has implications for non-commutative theories and
discrete quantum gravity. In the latter case, the present model can be viewed
as a top-down realization of a quantum-discrete to classical-continuum
transition.Comment: 1+82 pages, 1 figure, 2 tables. v2-3: discussions clarified and
improved (especially section 4.5), typos corrected, references added; v4:
further typos correcte
Varying constants, Gravitation and Cosmology
Fundamental constants are a cornerstone of our physical laws. Any constant
varying in space and/or time would reflect the existence of an almost massless
field that couples to matter. This will induce a violation of the universality
of free fall. It is thus of utmost importance for our understanding of gravity
and of the domain of validity of general relativity to test for their
constancy. We thus detail the relations between the constants, the tests of the
local position invariance and of the universality of free fall. We then review
the main experimental and observational constraints that have been obtained
from atomic clocks, the Oklo phenomenon, Solar system observations, meteorites
dating, quasar absorption spectra, stellar physics, pulsar timing, the cosmic
microwave background and big bang nucleosynthesis. At each step we describe the
basics of each system, its dependence with respect to the constants, the known
systematic effects and the most recent constraints that have been obtained. We
then describe the main theoretical frameworks in which the low-energy constants
may actually be varying and we focus on the unification mechanisms and the
relations between the variation of different constants. To finish, we discuss
the more speculative possibility of understanding their numerical values and
the apparent fine-tuning that they confront us with.Comment: 145 pages, 10 figures, Review for Living Reviews in Relativit