139 research outputs found
New Trends in Differential and Difference Equations and Applications
This is a reprint of articles from the Special Issue published online in the open-access journal Axioms (ISSN 2075-1680) from 2018 to 2019 (available at https://www.mdpi.com/journal/axioms/special issues/differential difference equations)
Families of exact solutions to Vasiliev's 4D equations with spherical, cylindrical and biaxial symmetry
We provide Vasiliev's four-dimensional bosonic higher-spin gravities with six
families of exact solutions admitting two commuting Killing vectors. Each
family contains a subset of generalized Petrov Type-D solutions in which one of
the two so(2) symmetries enhances to either so(3) or so(2,1). In particular,
the spherically symmetric solutions are static and we expect one of them to be
gauge-equivalent to the extremal Didenko-Vasiliev solution given in
arXiv:0906.3898. The solutions activate all spins and can be characterized
either via generalized electric and magnetic charges defined asymptotically in
weak-field regions or via the values of fully higher-spin gauge-invariant
observables given by on-shell closed zero-forms. The solutions are obtained by
combining the gauge-function method with separation of variables in twistor
space via expansion of the Weyl zero-form in Di-Rac supersingleton projectors
times deformation parameters in a fashion that is suggestive of a generalized
electromagnetic duality.Comment: v1: 77 pages; 3 tables; 23 pages of appendices. v2: 5 additional
pages of clarifications, typos correcte
Extreme Regimes in Quantum Gravity
The thesis is divided into two parts. In the first part the low-energy limit
of quantum gravity is analysed, whereas in the second we deal with the
high-energy domain. In the first part, by applying the effective field theory
point of view to the quantization of general relativity, detectable, though
tiny, quantum effects in the position of Newtonian Lagrangian points of the
Earth-Moon system are found. In order to make more realistic the quantum
corrected model proposed, the full three-body problem where the Earth and the
Moon interact with a generic massive body and the restricted four-body problem
involving the perturbative effects produced by the gravitational presence of
the Sun in the Earth-Moon system are also studied. After that, a new quantum
theory having general relativity as its classical counterpart is analysed. By
exploiting this framework, an innovative interesting prediction involving the
position of Lagrangian points within the context of general relativity is
described. Furthermore, the new pattern provides quantum corrections to the
relativistic coordinates of Earth-Moon libration points of the order of few
millimetres. The second part of the thesis deals with the Riemannian curvature
characterizing the boosted form assumed by the Schwarzschild-de Sitter metric.
The analysis of the Kretschmann invariant and the geodesic equation shows that
the spacetime possesses a "scalar curvature singularity" within a 3-sphere and
that it is possible to define what we here call "boosted horizon", a sort of
elastic wall where all particles are surprisingly pushed away, suggesting that
such "boosted geometries" are ruled by a sort of "antigravity effect".
Eventually, the equivalence with the coordinate shift method is invoked in
order to demonstrate that all terms appearing in the Riemann
curvature tensor give vanishing contribution in distributional sense.Comment: Phd thesis in Fundamental and Applied Physics presented at University
"Federico II" (Naples, Italy) on 29th April 201
A methodology for robust optimization of low-thrust trajectories in multi-body environments
Issued as final reportThales Alenia Spac
Estimation and control of non-linear and hybrid systems with applications to air-to-air guidance
Issued as Progress report, and Final report, Project no. E-21-67
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