Andrzej Trautman

Some spherical gravitational waves in general relativity

Einsteins equations for empty space are solved for the class of metrics which admit a family of hypersurface-orthogonal, non-shearing, diverging null curves. Some of these metrics may be considered as representing a simple kind of spherical, outgoing radiation. (Among them are solutions admitting no Killing field whatsoever.) Examples of solutions to the Maxwell-Einstein equations with a similar geometry are also given.

Solutions of the Maxwell and Yang-Mills equations associated with hopf fibrings

It is shown that the magnetic pole of lowest strength and the pseudoparticle solution of the Yang-Mills equations correspond to natural connections defined on the principal bundlesU(2)/U(1)=S3 →S2 andSp(2)/Sp(1)=S7 →S4, respectively. This observation leads to a general methods of constructing new, topologically nontrivial solutions of the Maxwell and Yang-Mills equations. Among them is an “electromagnetic instanton” defined over the two-dimensional complex projective space endowed with the Fubini-Study metric.

Noether equations and conservation laws

AbstractThe purpose of the paper is to present a rigorous derivation of the relation between conservation laws and transformations leaving invariant the action integral. The (space-)time development of a physical system is represented by a cross section of a product bundleM. A Lagrange function is defined as a mapping

Theory of Gravitation

L:\overline M \to R

Lectures on General Relativity

where

Fock space description of simple spinors

\overline M