60 70 19 v 1 1 2 Ju l 1 99 6 NBI preprint Nr

ar X iv : q - a lg / 9 60 70 28 v 1 2 7 Ju l 1 99 6 Examples of Categorification

ar X iv : h ep - l at / 9 60 70 64 v 1 2 6 Ju l 1 99 6

We present results from magnetic monopoles in SU (2) lattice gauge theory at finite temperature. The lattices are 16 3 × N t , for N t = 4, 6, 8, 12, at β = 2.5115. Quantities discussed are: the spacial string tension, Polyakov loops, and the screening of timelike and spacelike magnetic currents.

ar X iv : g r - qc / 9 70 70 27 v 2 2 9 Ju l 1 99 7 CGPG - 97 / 7 - 1 Black Holes with Short Hair

We present spherically symmetric black hole solutions for Einstein gravity coupled to anisotropic matter. We show that these black holes have arbitrarily short hair, and argue for stability by showing that they can arise from dynamical collapse. We also show that a recent ‘no short hair’ theorem does not apply to these solutions. Pacs numbers: 04.20.Jb, 04.40.Nr, 04.70.Bw Typeset using REVTEX

ar X iv : h ep - l at / 9 70 60 19 v 1 2 6 Ju n 19 97 BUTP – 97 / 16 Properties of Renormalization Group Transformations 1

We describe some properties of Renormalization Group transformations. Especially we show why some of the RG transformations have redundant eigenoperators with eigenvalues that cannot be determined by simple dimensional analysis and give the corresponding formulae. Work supported in part by Schweizerischer Nationalfonds

ar X iv : g r - qc / 9 70 70 27 v 1 1 3 Ju l 1 99 7 CGPG - 97 / 7 - 1 Black Holes with Short Hair

We present spherically symmetric black hole solutions for Einstein gravity coupled to anisotropic matter. We show that these black holes have arbitrarily short hair, and argue for stability by showing that they can arise from dynamical collapse. We also show that a recent ‘no short hair’ theorem does not apply to these solutions. Pacs numbers: 04.20.Jb, 04.40.Nr, 04.70.Bw Typeset using REVTEX