Building on the results of a previous paper, we compute for the first time a full first-order perturbative solution for the angular coordinates in the restricted post-Newtonian two-body problem with ...spin. The analytical integration of the angular coordinates, based on the theory of the Weierstrassian functions, allows us to investigate thoroughly the spin-orbit and spin-spin interactions, and to derive several new results. The application of our solution to a selection of idealized physical systems of interest reveals a rich variety of dynamical behaviours driven by purely relativistic effects. In particular, we highlight a new relativistic nutational motion resulting from the combined spin-orbit and spin-spin interactions.
We apply the 1 + 1 + 2 covariant approach to describe a general static and spherically symmetric relativistic stellar object which contains two interacting fluids. We then use the 1 + 1 + 2 equations ...to derive the corresponding Tolman-Oppenheimer-Volkoff equations in covariant form in the isotropic noninteracting case. These equations are used to obtain new exact solutions by means of direct resolution and reconstruction techniques. Finally, we show that the generating theorem known for the single-fluid case can also be used to obtain two-fluid solutions from single-fluid ones.
Abstract
We present a tetrad–affine approach to
f
(
Q
)
gravity coupled to spinor fields of spin-
1
2
. After deriving the field equations, we derive the conservation law of the spin density, showing ...that the latter ensures the vanishing of the antisymmetric part of the Einstein-like equations, just as it happens in theories with torsion and metricity. We then focus on Bianchi type-I cosmological models proposing a general procedure to solve the corresponding field equations and providing analytical solutions in the case of gravitational Lagrangian functions of the kind
f
(
Q
)
=
α
Q
n
. At late time such solutions are seen to isotropize and, depending on the value of the exponent
n
, they can undergo an accelerated expansion of the spatial scale factors.
We examine the post-Newtonian limit of the minimal exponential measure (MEMe) model presented in J. C. Feng, S. Carloni, Phys. Rev. D 101, 064002 (2020) using an extension of the parameterized ...post-Newtonian (PPN) formalism which is also suitable for other type-I minimally modified gravity theories. The new PPN expansion is then used to calculate the monopole term of the post-Newtonian gravitational potential and to perform an analysis of circular orbits within spherically symmetric matter distributions. The latter shows that the behavior does not differ significantly from that of general relativity for realistic values of the MEMe model parameter q . Instead the former shows that one can use precision measurements of Newton's constant G to improve the constraint on q by up to 10 orders of magnitude.
We revisit the relativistic restricted two-body problem with spin employing a perturbation scheme based on Lie series. Starting from a post-Newtonian expansion of the field equations, we develop a ...first-order secular theory that reproduces well-known relativistic effects such as the precession of the pericentre and the Lense-Thirring and geodetic effects. Additionally, our theory takes into full account the complex interplay between the various relativistic effects, and provides a new explicit solution of the averaged equations of motion in terms of elliptic functions. Our analysis reveals the presence of particular configurations for which non-periodical behaviour can arise. The application of our results to real astrodynamical systems (such as Mercury-like and pulsar planets) highlights the contribution of relativistic effects to the long-term evolution of the spin and orbit of the secondary body.
We extend Derrick's theorem to the case of a generic irrotational curved spacetime adopting a strategy similar to the original proof. We show that a static relativistic star made of real scalar ...fields is never possible regardless of the geometrical properties of the (static) spacetimes. The generalized theorem offers a tool that can be used to check the stability of localized solutions of a number of types of scalar field models as well as of compact objects of theories of gravity with a nonminimally coupled scalar degree of freedom.
Ordinal Neural Networks Without Iterative Tuning Fernandez-Navarro, Francisco; Riccardi, Annalisa; Carloni, Sante
IEEE transaction on neural networks and learning systems,
11/2014, Letnik:
25, Številka:
11
Journal Article
Ordinal regression (OR) is an important branch of supervised learning in between the multiclass classification and regression. In this paper, the traditional classification scheme of neural network ...is adapted to learn ordinal ranks. The model proposed imposes monotonicity constraints on the weights connecting the hidden layer with the output layer. To do so, the weights are transcribed using padding variables. This reformulation leads to the so-called inequality constrained least squares (ICLS) problem. Its numerical solution can be obtained by several iterative methods, for example, trust region or line search algorithms. In this proposal, the optimum is determined analytically according to the closed-form solution of the ICLS problem estimated from the Karush-Kuhn-Tucker conditions. Furthermore, following the guidelines of the extreme learning machine framework, the weights connecting the input and the hidden layers are randomly generated, so the final model estimates all its parameters without iterative tuning. The model proposed achieves competitive performance compared with the state-of-the-art neural networks methods for OR.
We present an analysis of the phase space of cosmological models based on a non-minimal coupling between the geometry and a fermionic condensate. We observe that the strong constraint coming from the ...Dirac equations allows a detailed design of the cosmology of these models, and at the same time guarantees an evolution towards a state indistinguishable from general relativistic cosmological models. In this light, we show in detail how the use of some specific potentials can naturally reproduce a phase of accelerated expansion. In particular, we find for the first time that an exponential potential is able to induce two de Sitter phases separated by a power law expansion, which could be an interesting model for the unification of an inflationary phase and a dark energy era.
The standard model of cosmology is based on homogeneous-isotropic solutions of Einstein's equations. These solutions are known to be gravitationally unstable to local inhomogeneous perturbations, ...commonly described as evolving on a background given by the same solutions. In this picture, the Friedmann-Lemaitre-Robertson-Walker (FLRW) backgrounds are taken to describe the average over inhomogeneous perturbations for all times. We study in this paper the (in)stability of FLRW dust backgrounds within a class of averaged inhomogeneous cosmologies. We examine the phase portraits of the latter, discuss their fixed points and orbital structure and provide detailed illustrations. We show that FLRW cosmologies are unstable in some relevant cases: averaged models are driven away from them through structure formation and accelerated expansion. We find support for the proposal that the dark components of the FLRW framework may be associated with these instability sectors. Our conclusion is that FLRW cosmologies have to be considered critically for their role to serve as reliable models for the physical background.
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