3,986 research outputs found

### Weak Gravitational Lensing in Fourth Order Gravity

For a general class of analytic
$f(R,R_{\alpha\beta}R^{\alpha\beta},R_{\alpha\beta\gamma\delta}R^{\alpha\beta\gamma\delta})$
we discuss the gravitational lensing in the Newtonian Limit of theory. From the
properties of Gauss Bonnet invariant it is successful to consider only two
curvature invariants between the Ricci and Riemann tensor. Then we analyze the
dynamics of photon embedded in a gravitational field of a generic
$f(R,R_{\alpha\beta}R^{\alpha\beta})$-Gravity. The metric is time independent
and spherically symmetric. The metric potentials are Schwarzschild-like, but
there are two additional Yukawa terms linked to derivatives of $f$ with respect
to two curvature invariants. Considering the case of a point-like lens, and
after of a generic matter distribution of lens, we study the deflection angle
and the images angular position. Though the additional Yukawa terms in the
gravitational potential modifies dynamics with respect to General Relativity,
the geodesic trajectory of photon is unaffected by the modification in the
action by only $f(R)$. While we find different results (deflection angle
smaller than one of General Relativity) only thank to introduction of a generic
function of Ricci tensor square. Finally we can affirm the lensing phenomena
for all $f(R)$-Gravities are equal to the ones known from General Relativity.
We conclude the paper showing and comparing the deflection angle and image
positions for $f(R,R_{\alpha\beta}R^{\alpha\beta})$-Gravity with respect to
ones of General Relativity.Comment: 11 pages, 5 figure

### Conformal Transformations and Weak Field Limit of Scalar-Tensor Gravity

The weak field limit of scalar tensor theories of gravity is discussed in
view of conformal transformations. Specifically, we consider how physical
quantities, like gravitational potentials derived in the Newtonian
approximation for the same scalar-tensor theory, behave in the Jordan and in
the Einstein frame. The approach allows to discriminate features that are
invariant under conformal transformations and gives contributions in the debate
of selecting the true physical frame. As a particular example, the case of
$f(R)$ gravity is considered.Comment: 11 pages, preliminary versio

### Galaxy rotation curves in $f(R,\phi)$-gravity

We investigate the possibility to explain theoretically the galaxy rotation
curves by a gravitational potential in total absence of dark matter. To this
aim an analytic fourth-order theory of gravity, nonminimally coupled with a
massive scalar field is considered. Specifically, the interaction term is given
by an analytic function $f(R,\phi)$ where $R$ is the Ricci scalar and $\phi$ is
the scalar field. The gravitational potential is generated by a point-like
source and compared with the so called Sanders's potential that can be exactly
reproduced in this case. This result means that the problem of dark matter in
spiral galaxies could be fully addressed by revising general relativity at
galactic scales and requiring further gravitational degrees of freedom instead
of new material components that have not been found out up to now.Comment: 17 pages, 6 figures. To appear in Phys. Rev.

### Fourth order gravity and experimental constraints on Eddington parameters

PPN-limit of higher order theories of gravity represents a still
controversial matter of debate and no definitive answer has been provided, up
to now, about this issue. By exploiting the analogy between scalar-tensor and
fourth-order theories of gravity, one can generalize the PPN-limit formulation.
By using the definition of the PPN-parameters $\gamma$ and $\beta$ in term of
the $f(R)$ derivatives, we show that a family of third-order polynomial
theories, in the Ricci scalar $R$, turns out to be compatible with the
PPN-limit and the deviation from General Relativity theoretically predicted
agree with experimental data.Comment: 7 pages, 3 figure

### The Quadratic Coefficient of the Electron Cloud Mapping

The Electron Cloud is an undesirable physical phenomenon which might produce
single and multi-bunch instability, tune shift, increase of pressure ultimately
limiting the performance of particle accelerators. We report our results on the
analytical study of the electron dynamics.Comment: 5 pages, 7 figures, presented at ECLOUD12: Joint
INFN-CERN-EuCARD-AccNet Workshop on Electron-Cloud Effects, La Biodola, Isola
d Elba, Italy, 5-9 June 201

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