Einstein vacuum field equations with a single non-null Killing vector

It is shown that, in the case where there is a single non-null Killing vector, the vacuum Einstein field equations imply that there is a Ricci collineation in the quotient 3-space. Using coordinates adapted to the collineation vector, we derive a fourth order partial differential equation involving the metric of the quotient 3-space and we show that if this equation is satisfied, the Ernst potential may be obtained by integrating a total Riccati equation and a straightforward set of total differential equations. We also show that if the collineation vector is null, the metric of the quotient 3-space may be expressed in terms of two real Clebsch potentials. Finally in the special case where the collineation vector is the generator of a timelike homothetic motion we reduce the field equations to a single second order partial differential equation of non-Painlevé type in two independent variables and obtain Petrov type III solution of Robinson-Trautman type.     

Reactions of ortho oxy-substituted benzyl and phenacyl bromides in dimethyl sulphoxide

o-Acetoxy- and o-benzoyloxy-benzyl bromides and tosylates oxidatively rearrange in moist dimethyl sulphoxide to o-hydroxybenzyl esters; o-acetoxy- and o-benzoyloxy- phenacyl bromides rearrange to mixtures of 2-hydroxycoumaran-3-ones and o-hydroxyphenacyl esters; o-hydroxyphenacyl bromides also yield 2-hydroxycoumaran-3-ones, together with o-hydroxyphenacyl alcohols. 2-Acetoxybenzaldehyde is reductively rearranged by sodium borohydride to o-hydroxybenzyl acetate.     

Multicomponent coupling approach to (+/-)-frondosin B and a ring-expanded analogue

[reaction: see text] A recently discovered multicomponent coupling reaction is used to give direct access to a late intermediate in the synthesis of frondosin B. This intermediate can also be efficiently converted to a ring-expanded analogue of frondosin B by sustained heating of the reaction mixture. An unprecedented tandem 1,7-hydrogen shift, 8pi-electrocyclization is proposed to explain the formation of this ring-expanded species.     

Synthesis and cross-coupling reactions of substituted 5-triflyloxyindoles

N-arylsulfonyl quinone monoimines undergo smooth cycloadditions in a [4+2] sense to yield the expected cycloadducts. The crude cycloadducts, when subjected to a short series of simple transformations, produce synthetically useful quantities of 5-triflyloxyindoles in excellent overall yields. Such compounds are excellent participants in cross-coupling chemistry.