To Pravda

This is a three part samizdat from Moscow by an anonymous author. The circumstances under which the samizdat was obtained were quite interesting. Several years ago an American professor was approached by a Moscovite in a subway station. Not speaking any Russian he was unable to understand what the man was saying to him. As the subway train approached the Soviet stuck some crumpled paper into the American\u27s pocket and disappeared. The professor did not realize until later that there was a developed negative of a film inside the paper. The negatives contained photos of many typed pages which, however, were illegible at the time due to the minute print. The film was eventually taken qut of the Soviet Union at considerable risk. After the film was develop�d and enlarged it became obvious that it is a rather interesting and sometimes bizarre piece of writing of a malcontent. Rqllo May observed that lunatics, artists, and prophets (not necessarily in that order) are the most perceptive sensors of societal maladies. They, before the rest of us, feel and express our collective experiences. Sections of the writing may strike us as the ramblings of a lunatic. Other parts are lucid, literate, but angry attacks at practically all that surrounds the author. The translation is a faithful rendition except for substitution of obscene words with euphemisms to protect the sensibilities of the average reader. We leave it to the readers to judge for themselves whether this samizdat adds to their knowledge of Soviet Life or not

Curvature invariants in type-III spacetimes

The results of paper [1] are generalized for vacuum type-III solutions with, in general, a non-vanishing cosmological constant Lambda. It is shown that all curvature invariants containing derivatives of the Weyl tensor vanish if a type-III spacetime admits a non-expanding and non-twisting null geodesic congruence. A non-vanishing curvature invariant containing first derivatives of the Weyl tensor is found in the case of type-III spacetime with expansion or twist.Comment: 1 reference added, typos corrected, accepted for publication in Clas. Quantum Gra

Subelliptic Estimates for Overdetermined Systems of Quadratic Differential Operators

We prove global subelliptic estimates for systems of quadratic differential operators. Quadratic differential operators are operators defined in the Weyl quantization by complex-valued quadratic symbols. In a previous work, we pointed out the existence of a particular linear subvector space in the phase space intrinsically associated to their Weyl symbols, called singular space, which rules a number of fairly general properties of non-elliptic quadratic operators. About the subelliptic properties of these operators, we established that quadratic operators with zero singular spaces fulfill global subelliptic estimates with a loss of derivatives depending on certain algebraic properties of the Hamilton maps associated to their Weyl symbols. The purpose of the present work is to prove similar global subelliptic estimates for overdetermined systems of quadratic operators. We establish here a simple criterion for the subellipticity of these systems giving an explicit measure of the loss of derivatives and highlighting the non-trivial interactions played by the different operators composing those systems.Comment: 37 page

Contraction semigroups of elliptic quadratic differential operators

We study the contraction semigroups of elliptic quadratic differential operators. Elliptic quadratic differential operators are the non-selfadjoint operators defined in the Weyl quantization by complex-valued elliptic quadratic symbols. We establish in this paper that under the assumption of ellipticity, as soon as the real part of their Weyl symbols is a non-zero non-positive quadratic form, the norm of contraction semigroups generated by these operators decays exponentially in time.Comment: 26 page

On the spinning C-metric

Physical interpretation of some stationary and non-stationary regions of the spinning C-metric is presented. They represent different spacetime regions of a uniformly accelerated Kerr black hole. Stability of geodesics corresponding to equilibrium points in a general stationary spacetime with an additional symmetry is also studied and results are then applied to the spinning C-metric.Comment: 12 pages, 7 figures, RevTeX

Curvature invariants in algebraically special spacetimes

It is well known that all curvature invariants of the order zero vanish for type-III and type-N vacuum spacetimes. We briefly summarize properties of higher order curvature invariants for these spacetimes.Comment: 2 pages, contribution to the 9th Marcel Grossmann meeting (MG9), Rome, July 200