5 research outputs found
On the 1/c Expansion of f(R) Gravity
We derive for applications to isolated systems - on the scale of the Solar
System - the first relativistic terms in the expansion of the space time
metric for metric gravity theories, where is assumed to
be analytic at . For our purpose it suffices to take into account up to
quadratic terms in the expansion of , thus we can approximate with a positive dimensional parameter . In the non-relativistic limit,
we get an additional Yukawa correction with coupling strength and Compton
wave length to the Newtonian potential, which is a known result in
the literature. As an application, we derive to the same order the correction
to the geodetic precession of a gyroscope in a gravitational field and the
precession of binary pulsars. The result of the Gravity Probe B experiment
yields the limit , whereas for the
pulsar B in the PSR J0737-3039 system we get a bound which is about
times larger. On the other hand the E\"ot-Wash experiment provides the best
laboratory bound . Although the former
bounds from geodesic precession are much larger than the laboratory ones, they
are still meaningful in the case some type of chameleon effect is present and
thus the effective values could be different at different length scales.Comment: 11 pages, accepted for publication in Physical Review
On Gravitational Radiation in Quadratic Gravity
We investigate the gravitational radiation emitted by an isolated system for
gravity theories with Lagrange density . As a formal result we
obtain leading order corrections to the quadrupole formula in General
Relativity. We make use of the analogy of theories with scalar--tensor
theories, which in contrast to General Relativity feature an additional scalar
degree of freedom. Unlike General Relativity, where the leading order
gravitational radiation is produced by quadrupole moments, the additional
degree of freedom predicts gravitational radiation of all multipoles, in
particular monopoles and dipoles, as this is the case for the most alternative
gravity theories known today. An application to a hypothetical binary pulsar
moving in a circular orbit yields the rough limit by constraining the dipole power to account at
most for 1% of the quadrupole power as predicted by General Relativity.Comment: 14 Pages, 1 Figur
On Gravitational Waves in Spacetimes with a Nonvanishing Cosmological Constant
We study the effect of a cosmological constant on the propagation
and detection of gravitational waves. To this purpose we investigate the
linearised Einstein's equations with terms up to linear order in in a
de Sitter and an anti-de Sitter background spacetime. In this framework the
cosmological term does not induce changes in the polarization states of the
waves, whereas the amplitude gets modified with terms depending on .
Moreover, if a source emits a periodic waveform, its periodicity as measured by
a distant observer gets modified. These effects are, however, extremely tiny
and thus well below the detectability by some twenty orders of magnitude within
present gravitational wave detectors such as LIGO or future planned ones such
as LISA.Comment: 8 pages, 4 figures, accepted for publication in Physical Review
On a class of law invariant convex risk measures
Law invariant convex risk measures, Robust representation, Variational methods, 91G99, D81, G22,