arXiv subjects

Simone Calogero

Publications and source records attributed to Simone Calogero.

At least 19 recordsLinked to original sources

arXiv2026

Collision geometry of relativistic spinning particles

We investigate elastic binary collisions of relativistic spinning particles in special relativity. The spin of each particle is represented by an antisymmetric second order tensor. Assuming the conservation of total four momentum and total spin tensor, together with the mass shell and spin constraints, we formulate the collision problem in a fully Lorentz covariant setting. We show that the relativistic collision problem admits a simple geometric formulation, reducing the original system of conservation laws to the solution of a quadratic equation on a circle. This reduction yields a complete classification of the postcollisional states together with explicit reconstruction formulas for all postcollisional variables from the conserved quantities. In particular, there are generically only finitely many postcollisional states, with the maximal number equal to eight.

math-ph↗

arXiv2025

Nonlinear diffusion in relativistic kinetic theory

A nonlinear Lorentz invariant kinetic diffusion equation is introduced, which is consistent with the conservation laws of particles number, energy and momentum. The equilibrium solution converges to the Maxwellian density in the Newtonian limit, but it is not given by the J\"uttner distribution commonly employed in relativistic kinetic theory. The nonlinear kinetic diffusion equation on a general Lorentzian manifold is consistent with the contracted Bianchi identities and therefore can be coupled to the Einstein equations of general relativity.

gr-qc↗

arXiv2024

Kinetic dynamics of neutral spin particles in a spacetime with torsion

A kinetic model for the dynamics of collisionless spin neutral particles in a spacetime with torsion is proposed. The fundamental matter field is the kinetic density $f(x,u,s)$ of particles with four-velocity $u$ and four-spin $s$. The stress-energy tensor and the spin current of the particles distribution are defined as suitable integral moments of $f$ in the $(u,s)$ variables. By requiring compatibility with the contracted Bianchi identity in Einstein-Cartan theory, we derive a transport equation on the kinetic density $f$ that generalizes the well-known Vlasov equation for spinless particles. The total number of particles in the new model is not conserved. To restore this important property we assume the existence in spacetime of a second species of particles with the same mass and spin magnitude. The Vlasov equation on the kinetic density $\overline{f}$ of the new particles is derived by requiring that the sum of total numbers of particles of the two species should be conserved.

gr-qc↗

arXiv2021

Self-gravitating static balls of power-law elastic matter

We study a class of power-law stored energy functions for spherically symmetric elastic bodies that includes well-known material models, such as the Saint Venant-Kirchhoff, Hadamard, Signorini and John models. We identify a finite subclass of these stored energy functions, which we call Lam\'e type, that depend on no more material parameters than the bulk modulus $\kappa>0$ and the Poisson ratio $-1<\nu\leq1/2$. A general theorem proving the existence of static self-gravitating elastic balls for some power-law materials has been given elsewhere. In this paper numerical evidence is provided that some hypotheses in this theorem are necessary, while others are not.

math-ph↗

arXiv2021

On self-gravitating polytropic elastic balls

A new four-parameters family of constitutive functions for spherically symmetric elastic bodies is introduced which extends the two-parameters class of polytropic fluid models widely used in several applications of fluid mechanics. The four parameters in the polytropic elastic model are the polytropic exponent $\gamma$, the bulk modulus $\kappa$, the shear exponent $\beta$ and the Poisson ratio $\nu\in (-1,1/2]$. The two-parameters class of polytropic fluid models arises as a special case when $\nu=1/2$ and $\beta=\gamma$. In contrast to the standard Lagrangian approach in elasticity theory, the polytropic elastic model in this paper is formulated directly in physical space, i.e., in terms of Eulerian state variables, which is particularly useful for the applications e.g. to astrophysics where the reference state of the bodies of interest (stars, planets, etc.) is not observable. After discussing some general properties of the polytropic elastic model, the steady states and the homologous motion of Newtonian self-gravitating polytropic elastic balls are investigated. It is shown numerically that static balls exist when the parameters $\gamma,\beta$ are contained in a particular region $\mathcal{O}$ of the plane, depending on $\nu$, and proved analytically for $(\gamma,\beta)\in\mathcal{V}$, where $\mathcal{V}\subset\mathcal{O}$ is a disconnected set which also depends on the Poisson ratio $\nu$. Homologous solutions describing continuously collapsing balls are constructed numerically when $\gamma=4/3$. The radius of these solutions shrinks to zero in finite time, causing the formation of a center singularity with infinite density and pressure. Expanding self-gravitating homologous elastic balls are also constructed analytically for some special values of the shear parameter $\beta$.

math.AP↗

arXiv2019

Static self-gravitating Newtonian elastic balls

The existence of static self-gravitating Newtonian elastic balls is proved under general assumptions on the constitutive equations of the elastic material. The proof uses methods from the theory of finite-dimensional dynamical systems and the Euler formulation of elasticity theory for spherically symmetric bodies introduced recently by the authors. Examples of elastic materials covered by the results of this paper are Saint Venant-Kirchhoff, John and Hadamard materials.

math-ph↗

arXiv2018

Multi-body spherically symmetric steady states of Newtonian self-gravitating elastic matter

We study the problem of static, spherically symmetric, self-gravitating elastic matter distributions in Newtonian gravity. To this purpose we first introduce a new definition of homogeneous, spherically symmetric (hyper)elastic body in Euler coordinates, i.e., in terms of matter fields defined on the current physical state of the body. We show that our definition is equivalent to the classical one existing in the literature and which is given in Lagrangian coordinates, i.e., in terms of the deformation of the body from a given reference state. After a number of well-known examples of constitutive functions of elastic bodies are re-defined in our new formulation, a detailed study of the Seth model is presented. For this type of material the existence of single and multi-body solutions is established.

math-ph↗

arXiv2018

Concentrating solutions of the relativistic Vlasov-Maxwell system

We study smooth, global-in-time solutions of the relativistic Vlasov-Maxwell system that possess arbitrarily large charge densities and electric fields. In particular, we construct spherically symmetric solutions that describe a thin shell of equally charged particles concentrating arbitrarily close to the origin and which give rise to charge densities and electric fields as large as one desires at some finite time. We show that these solutions exist even for arbitrarily small initial data or any desired mass. In the latter case, the time at which solutions concentrate can also be made arbitrarily large.

math-ph↗

arXiv2017

Arbitrarily large solutions of the Vlasov-Poisson system

We study smooth, global-in-time solutions of the Vlasov-Poisson system in the plasma physical case that possess arbitrarily large charge densities and electric fields. In particular, we construct two classes of solutions with this property. The first class are spherically-symmetric solutions that initially possess arbitrarily small density and field values, but attain arbitrarily large values of these quantities at some later time. Additionally, we construct a second class of spherically-symmetric solutions that possess any desired mass and attain arbitrarily large density and field values at any later prescribed time.

math.AP↗

arXiv2016

On the spatially homogeneous and isotropic Einstein-Vlasov-Fokker-Planck system with cosmological scalar field

The Einstein-Vlasov-Fokker-Planck system describes the kinetic diffusion dynamics of self-gravitating particles within the Einstein theory of general relativity. We study the Cauchy problem for spatially homogeneous and isotropic solutions and prove the existence of both global solutions and solutions that blow-up in finite time depending on the size of certain functions of the initial data. We also derive information on the large-time behavior of global solutions and toward the singularity for solutions which blow-up in fine time. Our results entail the existence of a phase of decelerated expansion followed by a phase of accelerated expansion, in accordance with the physical expectations in cosmology.

math.AP↗

arXiv2016

A stellar model with diffusion in general relativity

We consider a spherically symmetric stellar model in general relativity whose interior consists of a pressureless fluid undergoing microscopic velocity diffusion in a cosmological scalar field. We show that the diffusion dynamics compel the interior to be spatially homogeneous, by which one can infer immediately that within our model, and in contrast to the diffusion-free case, no naked singularities can form in the gravitational collapse. We then study the problem of matching an exterior Bondi type metric to the surface of the star and find that the exterior can be chosen to be a modified Vaidya metric with variable cosmological constant. Finally, we study in detail the causal structure of an explicit, self-similar solution.

gr-qc↗

arXiv2014

Dynamics of Robertson-Walker spacetimes with diffusion

We study the dynamics of spatially homogeneous and isotropic spacetimes containing a fluid undergoing microscopic velocity diffusion in a cosmological scalar field. After deriving a few exact solutions of the equations, we continue by analyzing the qualitative behavior of general solutions. To this purpose we recast the equations in the form of a two dimensional dynamical system and perform a global analysis of the flow. Among the admissible behaviors, we find solutions that are asymptotically de-Sitter both in the past and future time direction and which undergo accelerated expansion at all times.

gr-qc↗

arXiv2014

Exploring non-linear cosmological matter diffusion coefficients

Since microscopic velocity diffusion can be incorporated into general relativity in a consistent way, we study cosmological background solutions when the diffusion phenomena takes place in an expanding universe. Our focus here relies on the nature of the diffusion coefficient $\sigma$ which measures the magnitude of such transport phenomena. We test dynamics where $\sigma$ has a phenomenological dependence on the scale factor, the matter density, the dark energy and the expansion rate.

astro-ph.CO↗

arXiv2014

Spatially homogeneous solutions of the Vlasov-Nordstr\"om-Fokker-Planck system

The Vlasov-Nordstr\"{o}m-Fokker-Planck system describes the evolution of self-gravitating matter experiencing collisions with a fixed background of particles in the framework of a relativistic scalar theory of gravitation. We study the spatially-homogeneous system and prove global existence and uniqueness of solutions for the corresponding initial value problem in three momentum dimensions. Additionally, we study the long time asymptotic behavior of the system and prove that even in the absence of friction, solutions possess a non-trivial asymptotic profile. An exact formula for the long time limit of the particle density is derived in the ultra-relativistic case.

math-ph↗

arXiv2014

Spherically symmetric steady states of John elastic bodies in general relativity

We study some properties of static spherically symmetric elastic bodies in general relativity using both analytical and numerical tools. The materials considered belong to the class of John elastic materials and reduce to perfect fluids when the rigidity parameter is set to zero. We find numerical support that such elastic bodies exist with different possible shapes (balls, single shells and multiple shells) and that their gravitational redshift can be very large ($z\approx 2.8$) without violating the dominant energy condition. Moreover we show that the elastic body has finite radius even in the case when the constitutive equation of the elastic material is a perturbation of a polytropic fluid without finite radius, thereby concluding that such fluids are structurally unstable within the larger class of elastic matter models under study.

gr-qc↗

arXiv2013

Cosmology with matter diffusion

We construct a viable cosmological model based on velocity diffusion of matter particles. In order to ensure the conservation of the total energy-momentum tensor in the presence of diffusion, we include a cosmological scalar field $\phi$ which we identify with the dark energy component of the Universe. The model is characterized by only one new degree of freedom, the diffusion parameter $\sigma$. The standard $\Lambda$CDM model can be recovered by setting $\sigma=0$. If diffusion takes place ($\sigma >0$) the dynamics of the matter and of the dark energy fields are coupled. We argue that the existence of a diffusion mechanism in the Universe can serve as a theoretical motivation for interacting models. We constrain the background dynamics of the diffusion model with Supernovae, H(z) and BAO data. We also perform a perturbative analysis of this model in order to understand structure formation in the Universe. We calculate the impact of diffusion both on the CMB spectrum, with particular attention to the integrated Sachs-Wolfe signal, and on the matter power spectrum $P(k)$. The latter analysis places strong constraints on the magnitude of the diffusion mechanism but does not rule out the model.

astro-ph.CO↗

arXiv2012

Ground states of self-gravitating elastic bodies

The existence of static, self-gravitating elastic bodies in the non-linear theory of elasticity is established. Equilibrium configurations of self-gravitating elastic bodies close to the reference configuration have been constructed in [6] using the implicit function theorem. In contrast, the steady states considered in this article correspond to deformations of the relaxed state with no size restriction and are obtained as minimizers of the energy functional of the elastic body.

math-ph↗

arXiv2012

Cosmological models with fluid matter undergoing velocity diffusion

A new type of fluid matter model in general relativity is introduced, in which the fluid particles are subject to velocity diffusion without friction. In order to compensate for the energy gained by the fluid particles due to diffusion, a cosmological scalar field term is added to the left hand side of the Einstein equations. This hypothesis promotes diffusion to a new mechanism for accelerated expansion in cosmology. It is shown that diffusion alters not only quantitatively, but also qualitatively the global dynamical properties of the standard cosmological models.

gr-qc↗