One entropy function to rule them all

We study the entropy of extremal four dimensional black holes and five dimensional black holes and black rings is a unified framework using Sen's entropy function and dimensional reduction. The five dimensional black holes and black rings we consider project down to either static or stationary black holes in four dimensions. The analysis is done in the context of two derivative gravity coupled to abelian gauge fields and neutral scalar fields. We apply this formalism to various examples including $U(1)^3$ minimal supergravity.Comment: 29 pages, 2 figures, revised version for publication, details adde

Extremal single-charge small black holes: Entropy function analysis

We study stretched horizons of the type AdS_2 x S^8 for certain spherically symmetric extremal small black holes in type IIA carrying only D0-brane charge making use of Sen's entropy function formalism for higher derivative gravity. A scaling argument is given to show that the entropy of this class of black holes for large charge behaves as \sqrt{|q|} where q is the electric charge. The leading order result arises from IIA string loop corrections. We find that for solutions to exist the force on a probe D0-brane has to vanish and we prove that this feature persists to all higher derivative orders. We comment on the nature of the extremum of these solutions and on the sub-leading corrections to the entropy. The entropy of other small black holes related by dualities to our case is also discussed.Comment: 19 pages, v2:typos corrected and references adde

Kinetics of enzyme attack on substrates covalently attached to solid surfaces : influence of spacer chain length, immobilised substrate surface concentration and surface charge

The use of α-chymotrypsin to cleave covalently bound N-acetyl-L-tryptophan (Ac-Trp-OH) from the surfaces of aminopropylated controlled pore glass (CPG) and the polymer PEGA1900 was investigated. Oligoglycine spacer chains were used to present the covalently attached Ac-Trp-OH substrate to the aqueous enzyme. In the absence of the oligoglycine spacer chain, the rate of release was relatively slow, especially from the PEGA1900. These slow rates reflect the position of the amino group to which Ac-Trp-OH is covalently attached. On the glass there was a clear optimum with a chain of four glycine residues. For PEGA1900 there is no real apparent change beyond two glycine residues. The decline in rate beyond these optima are a possible result of changes in oligoglycine structure. Comparing different surface loadings of bound substrate, the rate of release of Ac-Trp-OH from CPG with a pore diameter of 1200 Å was optimal when using 83% of the maximum that can be coupled, then fell again at higher loading. The rate of Ac-Trp-OH release from CPG was the same for surface coverage's of 0.4 and 1.0. The introduction of permanent surface charges on CPG1200 exhibits a distinct influence on enzymatic cleavage with an increase in the rate of biocatalysis at the surface. Optimal presentation of covalently immobilised substrate on different supports by use of appropriate linkers leads to favourable biocatalysis from the support