Singularities^59Negative- tens ion Posit he-te nsio n
Brane B rane
3.1.6 Higher dimensional resolutions
Serini, Einstein, Pauli and Lichnerowicz were able to show that there are no static or
stationary soliton like solutions of the vacuum Einstein equations without horizons
(see [45] for a review of this type of result). The presence of an horizon implies a
singularity. These results extend straightforwardly [45] to include the sort of matter
encountered in ungauged supergravity theories and Klauza-Klein theory7 or the zero
slope limits of String Theory. They follow essentially because these theories do not
admit a length scale: rigid dilation
(12)
gbLV ---f X^2 gbv X constant,is a symmetry of the equations of motion.
7with the proviso that the fields in four dimensions are regular, see later