Morphology of the two-dimensional MRI in Axial Symmetry

In this paper, we analyze the linear stability of a stellar accretion disk, having a stratified morphology. The study is performed in the framework of ideal magneto-hydrodynamics and therefore it results in a characterization of the linear unstable magneto-rotational modes. The peculiarity of the present scenario consists of adopting the magnetic flux function as the basic dynamical variable. Such a representation of the dynamics allows to make account of the co-rotation theorem as a fundamental feature of the ideal plasma equilibrium, evaluating its impact on the perturbation evolution too. According to the Alfvenic nature of the Magneto-rotational instability, we consider an incompressible plasma profile and perturbations propagating along the background magnetic field. Furthermore, we develop a local perturbation analysis, around fiducial coordinates of the background configuration and dealing with very small scale of the linear dynamics in comparison to the background inhomogeneity size. The main issue of the present study is that the condition for the emergence of unstable modes is the same in the stratified plasma disk, as in the case of a thin configuration. Such a feature is the result of the cancelation of the vertical derivative of the disk angular frequency from the dispersion relation, which implies that only the radial profile of the differential rotation is responsible for the trigger of growing modes.Comment: 7 pages, 0 figures, 2015 Workshop "Complex plasma phenomena in the laboratory and in the universe

Implications of the Co-rotation Theorem on the MRI in Axial Symmetry

We analyze the linear stability of an axially symmetric ideal plasma disk, embedded in a magnetic field and endowed with a differential rotation. This study is performed by adopting the magnetic flux function as the fundamental dynamical variable, in order to outline the role played by the co-rotation theorem on the linear mode structure. Using some specific assumptions (e.g. plasma incompressibility and propagation of the perturbations along the background magnetic field), we select the Alfvenic nature of the Magneto-Rotational Instability and, in the geometric optics limit, we determine the dispersion relation describing the linear spectrum. We show how the implementation of the co-rotation theorem (valid for the background configuration) on the linear dynamics produces the cancellation of the vertical derivative of the disk angular velocity (we check such a feature also in the standard vector formalism to facilitate comparison with previous literature, both in the axisymmetric and three-dimensional case). As a result, we clarify that the unstable modes have, for a stratified disk, the same morphology, proper of a thin disk profile, and the $z$ dependence has a simple parametric role.Comment: 10 pages. Major modification

Squeezing of toroidal accretion disks

Accretion disks around very compact objects such as very massive Black hole can grow according to thick toroidal models. We face the problem of defining how does change the thickness of a toroidal accretion disk spinning around a Schwarzschild Black hole under the influence of a toroidal magnetic field and by varying the fluid angular momentum. We consider both an hydrodynamic and a magnetohydrodynamic disk based on the Polish doughnut thick model. We show that the torus thickness remains basically unaffected but tends to increase or decrease slightly depending on the balance of the magnetic, gravitational and centrifugal effects which the disk is subjected to.Comment: 6 pages, 17 figures, to appear in EP

Exponential Lagrangian for the Gravitational Field and the problem of Vacuum Energy

We will analyze two particular features of an exponential gravitational Lagrangian. On the one hand, while this choice of the Lagrangian density allows for two free parameters, only one scale, the cosmological constant, arises as fundamental when the proper Einsteinian limit is to be recovered. On the other hand, the vacuum energy arising from $f(R)$ theories such that $f(0)\neq 0$ needs a cancellation mechanism, by which the present value of the cosmological constant can be recast.Comment: 4 pages, to appear in Proceedings of the II Stueckelberg Workshop - Int. J. Mod. Phys.

Non-analytical power law correction to the Einstein-Hilbert action: gravitational wave propagation

We analyze the features of the Minkowskian limit of a particular non-analytical f(R) model, whose Taylor expansion in the weak field limit does not hold, as far as gravitational waves (GWs) are concerned. We solve the corresponding Einstein equations and we find an explicit expression of the modified GWs as the sum of two terms, i.e. the standard one and a modified part. As a result, GWs in this model are not transverse, and their polarization is different from that of General Relativity. The velocity of the GW modified part depends crucially on the parameters characterizing the model, and it mostly results much smaller than the speed of light. Moreover, this investigation allows one to further test the viability of this particular f(R) gravity theory as far as interferometric observations of GWs are concerned.Comment: 18 pages, 3 figure

On the Gravitational Collapse of a Gas Cloud in Presence of Bulk Viscosity

We analyze the effects induced by the bulk viscosity on the dynamics associated to the extreme gravitational collapse. Aim of the work is to investigate whether the presence of viscous corrections to the evolution of a collapsing gas cloud influence the fragmentation process. To this end we study the dynamics of a uniform and spherically symmetric cloud with corrections due to the negative pressure contribution associated to the bulk viscosity phenomenology. Within the framework of a Newtonian approach (whose range of validity is outlined), we extend to the viscous case either the Lagrangian, either the Eulerian motion of the system and we treat the asymptotic evolution in correspondence to a viscosity coefficient of the form $\zeta=\zeta_0 \rho^{nu}$ ($\rho$ being the cloud density and $\zeta_0=const.$). We show how, in the adiabatic-like behavior of the gas (i.e. when the politropic index takes values $4/3<\gamma\leq5/3$), density contrasts acquire, asymptotically, a vanishing behavior which prevents the formation of sub-structures. We can conclude that in the adiabatic-like collapse the top down mechanism of structures formation is suppressed as soon as enough strong viscous effects are taken into account. Such a feature is not present in the isothermal-like (i.e. $1\leq\gamma<4/3$) collapse because the sub-structures formation is yet present and outlines the same behavior as in the non-viscous case. We emphasize that in the adiabatic-like collapse the bulk viscosity is also responsible for the appearance of a threshold scale beyond which perturbations begin to increase.Comment: 13 pages, no figur

Oscillatory regime in the Multidimensional Homogeneous Cosmological Models Induced by a Vector Field

We show that in multidimensional gravity vector fields completely determine the structure and properties of singularity. It turns out that in the presence of a vector field the oscillatory regime exists in all spatial dimensions and for all homogeneous models. By analyzing the Hamiltonian equations we derive the Poincar\'e return map associated to the Kasner indexes and fix the rules according to which the Kasner vectors rotate. In correspondence to a 4-dimensional space time, the oscillatory regime here constructed overlap the usual Belinski-Khalatnikov-Liftshitz one.Comment: 9 pages, published on Classical and Quantum Gravit