Dynamics of viscous dissipative gravitational collapse: A full causal approach

The Misner and Sharp approach to the study of gravitational collapse is extended to the viscous dissipative case in, both, the streaming out and the diffusion approximations. The dynamical equation is then coupled to causal transport equations for the heat flux, the shear and the bulk viscosity, in the context of Israel--Stewart theory, without excluding the thermodynamics viscous/heat coupling coefficients. The result is compared with previous works where these later coefficients were neglected and viscosity variables were not assumed to satisfy causal transport equations. Prospective applications of this result to some astrophysical scenarios are discussed.Comment: 22 pages Latex. To appear in Int. J. Mod. Phys. D. Typos correcte

The Sagnac Effect in curved space-times from an analogy with the Aharonov-Bohm Effect

In the context of the natural splitting, the standard relative dynamics can be expressed in terms of gravito-electromagnetic fields, which allow to formally introduce a gravito-magnetic Aharonov-Bohm effect. We showed elsewhere that this formal analogy can be used to derive the Sagnac effect in flat space-time as a gravito-magnetic Aharonov-Bohm effect. Here, we generalize those results to study the General Relativistic corrections to the Sagnac effect in some stationary and axially symmetric geometries, such as the space-time around a weakly gravitating and rotating source, Kerr space-time, G\"{odel} universe and Schwarzschild space-time.Comment: 14 pages, 1 EPS figure, LaTeX, accepted for publication in General Relativity and Gravitatio

Conservation laws for vacuum tetrad gravity

Ten conservation laws in useful polynomial form are derived from a Cartan form and Exterior Differential System (EDS) for the tetrad equations of vacuum relativity. The Noether construction of conservation laws for well posed EDS is introduced first, and an illustration given, deriving 15 conservation laws of the free field Maxwell Equations from symmetries of its EDS. The Maxwell EDS and tetrad gravity EDS have parallel structures, with their numbers of dependent variables, numbers of generating 2-forms and generating 3-forms, and Cartan character tables all in the ratio of 1 to 4. They have 10 corresponding symmetries with the same Lorentz algebra, and 10 corresponding conservation laws.Comment: Final version with additional reference

Quantizing non-Lagrangian gauge theories: an augmentation method

We discuss a recently proposed method of quantizing general non-Lagrangian gauge theories. The method can be implemented in many different ways, in particular, it can employ a conversion procedure that turns an original non-Lagrangian field theory in $d$ dimensions into an equivalent Lagrangian topological field theory in $d+1$ dimensions. The method involves, besides the classical equations of motion, one more geometric ingredient called the Lagrange anchor. Different Lagrange anchors result in different quantizations of one and the same classical theory. Given the classical equations of motion and Lagrange anchor as input data, a new procedure, called the augmentation, is proposed to quantize non-Lagrangian dynamics. Within the augmentation procedure, the originally non-Lagrangian theory is absorbed by a wider Lagrangian theory on the same space-time manifold. The augmented theory is not generally equivalent to the original one as it has more physical degrees of freedom than the original theory. However, the extra degrees of freedom are factorized out in a certain regular way both at classical and quantum levels. The general techniques are exemplified by quantizing two non-Lagrangian models of physical interest.Comment: 46 pages, minor correction

Some analytical models of radiating collapsing spheres

We present some analytical solutions to the Einstein equations, describing radiating collapsing spheres in the diffusion approximation. Solutions allow for modeling physical reasonable situations. The temperature is calculated for each solution, using a hyperbolic transport equation, which permits to exhibit the influence of relaxational effects on the dynamics of the system.Comment: 17 pages Late

On magnetic field generation in Kolmogorov turbulence

We analyze the initial, kinematic stage of magnetic field evolution in an isotropic and homogeneous turbulent conducting fluid with a rough velocity field, v(l) ~ l^alpha, alpha<1. We propose that in the limit of small magnetic Prandtl number, i.e. when ohmic resistivity is much larger than viscosity, the smaller the roughness exponent, alpha, the larger the magnetic Reynolds number that is needed to excite magnetic fluctuations. This implies that numerical or experimental investigations of magnetohydrodynamic turbulence with small Prandtl numbers need to achieve extremely high resolution in order to describe magnetic phenomena adequately.Comment: 4 pages, revised, new material adde

Second order perturbation theory for embedded eigenvalues

We study second order perturbation theory for embedded eigenvalues of an abstract class of self-adjoint operators. Using an extension of the Mourre theory, under assumptions on the regularity of bound states with respect to a conjugate operator, we prove upper semicontinuity of the point spectrum and establish the Fermi Golden Rule criterion. Our results apply to massless Pauli-Fierz Hamiltonians for arbitrary coupling.Comment: 30 pages, 2 figure

Voltammetric characterization of gold-based bimetallic (AuPt; AuPd; AuAg) nanoparticles

Bimetallic nanoparticles are nowadays some of the most promising materials for catalytic, electrocatalytic and electroanalytical applications thanks to their novel optical, catalytic, magnetic, and sensing properties. Such novel features, often different and enhanced with respect to the monometallic counterparts, make these systems good candidates to be conveniently applied in a wide range of fields. The possibility to obtain different kinds of bimetallic composites (in terms of composition, structure, metal loading, morphology, etc.) goes in parallel with the need of powerful and accurate characterization tools. Among the commonly involved techniques like Optical Spectroscopy and Dynamic Light Scattering (DLS), also the more powerful Transmission Electron Microscopy (HR-TEM) and Extended X-Ray Absorption Fine Structure (EXAFS) are widely used. However, these analytical tools present some drawbacks in terms of high costs and low accessibility. In this context, electrochemistry and particularly Cyclic Voltammetry, is here proposed as an alternative, low cost, easy to use and simple characterization technique. The possibility to use electrochemical methods to study the final structure of bimetallic nanocomposites was already demonstrated in the Literature [1-2], but there is still lack of information on how such systems change and evolve in time and after aging periods. Therefore, Cyclic Voltammetry is here used, as a complementary technique to HR-TEM and EXAFS not only to investigate the structure of alloyed or core-shell gold-based (Au-Pt; Au-Pd; Au-Ag) systems (by studying the quantity and type of metals present in the materials), but also to elucidate the evolution and growth in time of such bimetallic samples. Time evolution characterization allows to control the morphology and to fix it at the desired point. Finally, the characterized gold-based nanocomposites are used in electrochemical sensing and electrocatalytic applications. A strong improvement in the response, in terms of higher peak currents and electrocatalytic effects, of the bimetallic systems with respect to the monometallic counterparts is evidenced, due to the intimate contact between the two metals, which is responsible of synergistic effects. Also, the effects of an eventual carbonaceous support on the properties of the metal nanoparticles and the possible synergistic effects between composites and supports are investigated [3]. [1] K. Tschulik, K. Ngamchuea, C. Ziegler, M.G. Beier, C. Damm, A. Eychmueller, R.G. Compton, Adv. Funct. Mater., 2015, 25, 5149\u20135158. [2] V. Pifferi, C. Chan-Thaw, S. Campisi, A. Testolin, A. Villa, L. Falciola, L. Prati, Molecules, 2016, 21, 261. [3] A. Testolin, S.Cattaneo, W. Wang, D. Wang, V. Pifferi, L. Prati, L. Falciola, A. Villa, Surfaces, 2019, 2, 205-215

Dynamics of dissipative gravitational collapse

The Misner and Sharp approach to the study of gravitational collapse is extended to the dissipative case in, both, the streaming out and the diffusion approximations. The role of different terms in the dynamical equation are analyzed in detail. The dynamical equation is then coupled to a causal transport equation in the context of Israel--Stewart theory. The decreasing of the inertial mass density of the fluid, by a factor which depends on its internal thermodynamics state, is reobtained, at any time scale. In accordance with the equivalence principle, the same decreasing factor is obtained for the gravitational force term. Prospective applications of this result to some astrophysical scenarios are discussed.Comment: Some misprints in eqs.(38) and (39) correcte

Non-Abelian Conversion and Quantization of Non-scalar Second-Class Constraints

We propose a general method for deformation quantization of any second-class constrained system on a symplectic manifold. The constraints determining an arbitrary constraint surface are in general defined only locally and can be components of a section of a non-trivial vector bundle over the phase-space manifold. The covariance of the construction with respect to the change of the constraint basis is provided by introducing a connection in the ``constraint bundle'', which becomes a key ingredient of the conversion procedure for the non-scalar constraints. Unlike in the case of scalar second-class constraints, no Abelian conversion is possible in general. Within the BRST framework, a systematic procedure is worked out for converting non-scalar second-class constraints into non-Abelian first-class ones. The BRST-extended system is quantized, yielding an explicitly covariant quantization of the original system. An important feature of second-class systems with non-scalar constraints is that the appropriately generalized Dirac bracket satisfies the Jacobi identity only on the constraint surface. At the quantum level, this results in a weakly associative star-product on the phase space.Comment: LaTeX, 21 page