abstract

A general Kerr–Schild metric \(g_{ik}= \eta _{ik} + H\xi _i\xi _k\) is considered in connection with Einstein–Maxwell field equations. The vector \(\xi _i\) generates a shear-free null geodetic congruence both in Minkowski space and in the Kerr–Schild space-times. In addition, we have assumed that \(\xi _i\) is hypersurface orthogonal. Two types of exact solutions are obtained. One is the solution for an accelerated charge given by Bonnor and Vaidya with a \({\mit \Lambda }\)-term. The other is a similar solution where a space-like curve plays the role of the time-like curve describing the world line of the accelerating charge. Taub’s solutions describing high-frequency gravitational radiation in Kerr–Schild space-times are derived as particular cases.

abstract

A uniform cosmological model filled with a fluid which possesses pressure and bulk viscosity is developed using extended thermodynamics. The Einstein and thermodynamic equations can be exactly integrated for Friedman-like situation. One of the solutions is non singular: it starts from a steady state behavior and expands to a situation where viscosity dies out.

abstract

Certain aspects of the pedagogical character of the Polyakov bosonic strings are discussed. In particular we use expansion in terms of the eigenfunctions of the operators \(\bigtriangledown ^2\), \(P^+P\) and \(PP^+\) to study: a) the ambiguity present in the definition of the path integral measure; b) Weyl invariance as the local property. Next, one-loop calculation is discussed and, as its new illustration, the dilaton tadpole amplitudes for open oriented and unoriented strings and the four-graviton amplitude for the closed oriented string are presented.

abstract

On the occasion of the 100th birthday of Erwin Schrodinger, an outline of his life and work is presented, together with an analysis of the steps that led him to wave mechanics.

abstract

Lagrangian and Hamiltonian descriptions of classical particles with spin and colour are presented. We take into account a new Classical observable which is due to a possible coupling between spin and colour degrees of freedom. In a configurational space of the particle we find a topologically non-trivial gauge structure related to a generalized Hopf fibration \(S^7 \to CP^3\).

abstract

Classical gauge fields (pure, coupled to the Dirac, scalar and gravitational fields) are investigated in the weak-coupling and strong-coupling limits. Several results concerning coupling constant dependence of fields in these regions are given. In particular, validity of the weak-coupling perturbative techniques is questioned for dynamical and non-singular solutions to the field equations.