Gas dynamics in strong gravitational fields

The steady and axially symmetric flow of a perfect fluid is studied in the context of general relativistic gas dynamics. It is assumed that the flow occurs in the background field of a rotating black hole (or any compact object). The hydrodynamic equations are referred to a locally nonrotating frame and their characteristics are found. The equations describing oblique shock waves are also obtained.     

Relativistic Quantum Correlations Between Spin-1/2 Particles

It is shown that a fully relativistic formulation of spin measurements and correlations does not add any new feature to the standard analysis of Bell and the deduction of his inequality. It follows, therefore, that the motion of reference frames does not affect the correlations between spatially separated particles.     

Thermal representation of the energy density in bounded spaces

The energy-momentum tensor of a quantum massless free field in a curved spacetime can be written in many cases as an integral with a thermal denominator and a modified phase-space numerator. It is shown that in general the thermal denominator is related to the bounded nature of the system, which in turn implies a representation of the energy density as an infinite numerable sum in Fock space. The modification of the phase-space density is related to the absence of long-wave contributions for nonzero values of the spin.     

Hamiltonian formulation of general relativity in terms of Dirac spinors

The Dirac spinors and matrices are used in combination with the Arnowitt-Deser-Misner formalism in order to obtain yet another formulation of Hamiltonian general relativity, together with a new form of the Gauss-Codazzi equations. The relation with Ashtekar's variables is analyzed; it is shown, for instance, that the matrices are equivalent to the electric field variable. The electric and magnetic decomposition of the gravitational field is also studie using Dirac matrices.     

Some type III solutions of the Einstein-Maxwell equations

A Petrov type III metric with nontwisting, degenerate Debever-Penrose direction is studied. This metric is, in general, a solution of the Einstein-Maxwell equations. Two particular cases are investigated in some detail. It is shown that the metric contains typeN, conformally flat and flat metrics as special subcases. Among these subcases, we find the metric of plane gravitational waves and the Bertotti-Robinson solution.     

Minimum uncertainty states in angular momentum and angle variables for charged particles in structured electromagnetic fields

We study the phase-space properties of a charged particle in a static electromagnetic field exhibiting vortex pairs with complementary topological charges and in a pure gauge field. A stationary solution of the Schrödinger equation that minimizes the uncertainty relations for angular momentum and trigonometric functions of the phase is obtained. It does not exhibit vortices and the angular momentum is due to the gauge field only. Increasing the topological charge of the vortices increases the regions where the Wigner function in the angle–angular momentum plane takes negative values, and thus enhances the quantum character of the dynamics.     

Coherent quantum states of a relativistic particle in an electromagnetic plane wave and a parallel magnetic field

We analyze the solutions of the Klein–Gordon and Dirac equations describing a charged particle in an electromagnetic plane wave combined with a magnetic field parallel to the direction of propagation of the wave. It is shown that the Klein–Gordon equation admits coherent states as solutions, while the corresponding solutions of the Dirac equation are superpositions of coherent and displaced-number states. Particular attention is paid to the resonant case in which the motion of the particle is unbounded.     

Effective Lagrangians in classical Yang-Mills theories

The formalism of nonlinear electrodynamics is adapted to the Yang-Mills field theory and it is shown that vacuum polarization effects can be described classically through an effective Lagrangian. As an example, an ad hoc Lagrangian is proposed which leads to a simple solution corresponding to a linear plus Coulomb type potential.