Essay: The Quantum Gravitational Black Hole Is Neither Black Nor White

Understanding the end state of black hole evaporation, the microscopic origin of black hole entropy, the information loss paradox, and the nature of the singularity arising in gravitational collapse - these are outstanding challenges for any candidate quantum theory of gravity. Recently, a midisuperspace model of quantum gravitational collapse has been solved using a lattice regularization scheme. It is shown that the mass of an eternal black hole follows the Bekenstein spectrum, and a related argument provides a fairly accurate estimate of the entropy. The solution also describes a quantized mass-energy distribution around a central black hole, which in the WKB approximation, is precisely Hawking radiation. The leading quantum gravitational correction makes the spectrum non-thermal, thus providing a plausible resolution of the information loss problem.     

Dirac-Hestenes spinor fields on Riemann-Cartan manifolds

In this paper we study Dirac-Hestenes spinor fields (DHSF) on a four-dimensional Riemann-Cartan spacetime (RCST). We prove that these fields must be defined as certain equivalence classes of even sections of the Clifford bundle (over the RCST), thereby being certain particular sections of a new bundle named the spin-Clifford bundle (SCB). The conditions for the existence of the SCB are studied and are shown to be equivalent to Geroch's theorem concerning the existence of spinor structures in a Lorentzian spacetime. We introduce also the covariant and algebraic Dirac spinor fields and compare these with DHSF, showing that all three kinds of spinor fields contain the same mathematical and physical information. We clarify also the notion of (Crumeyrolle's) amorphous spinors (Dirac-Kähler spinor fields are of this type), showing that they cannot be used to describe fermionic fields. We develop a rigorous theory for the covariant derivatives of Clifford fields (sections of the Clifford bundle, CB) and of Dirac-Hestenes spinor fields. We show how to generalize the original Dirac-Hestenes equation in Minkowski spacetime for the case of RCST. Our results are obtained from a variational principle formulated through the multiform derivative approach to Lagrangian field theory in the Clifford bundle.     

Oxidation of some catecholamines by sodium N-chloro-p-toluenesulfonamide in acid medium: A kinetic and mechanistic approach

The kinetics of the oxidation of five catecholamines viz., dopamine (A), L-dopa (B), methyldopa (C), epinephrine (D) and norepinephrine (E) by sodium N-chloro-p-toluenesulfonamide or chloramine-T (CAT) in presence of HClO₄ was studied at 30±0.1 °C. The five reactions followed identical kinetics with a first-order dependence on [CAT] _o , fractional-order in [substrate] _o , and inverse fractional-order in [H⁺]. Under comparable experimental conditions, the rate of oxidation of catecholamines increases in the order D>E>A>B>C. The variation of ionic strength of the medium and the addition of p-toluenesulfonamide or halide ions had no significant effect on the reaction rate. The rate increased with decreasing dielectric constant of the medium. The solvent isotope effect was studied using D₂O. A Michaelis-Menten type mechanism has been suggested to explain the results. Equilibrium and decomposition constants for CAT-catecholamine complexes have been evaluated. CH₃C₆H₄SO₂NHCl of the oxidant has been postulated as the reactive oxidizing species and oxidation products were identified. An isokinetic relationship is observed with β=361 K, indicating that enthalpy factors control the reaction rate. The mechanism proposed and the derived rate law are consistent with the observed kinetics.     

Hydrolysis of new phthalimide-derived esters catalyzed by immobilized lipase

The last step of the production of four phthalimide-derived acids, designed to act as antiasthma drugs, was performed by enzymatic hydrolysis of the respective methyl or ethyl esters. The esters 4-ethyl-[2-(1,3-dioxo-1,3-dihydro-2-isoindoylyl)]-phenoxyacetic methyl ester (PHT-MET), 4-ethyl-[2-(1,3-dioxo-1,3-dihydro-2-isoindoylyl)]-phenoxyacetic ethyl ester, 4-(1,3-dioxo-1,3-dihydro-2-isoindoylyl)-phenoxyacetic ethyl ester, and 2-(1,3-dioxo-1, 3-dihydro-2-isoindoylyl)-phenoxyacetic ethyl ester were hydrolyzed by immobilized lipase. The enzymatic reaction could be used only to produce the desired 4-substituted compounds. The best result that was found to hydrolysis of PHT-MET, and, therefore, that ester was selected for optimization experiments in a three-phase system. Reactions were performed with solid biocatalyst (Lipozyme® RM IM), organic solvent phase (ethyl acetate), and aqueous phase (saturated Na₂CO₃ solution). To optimize the reaction conditions, an experimental design optimization procedure was used. The variables studied were the amount of enzyme, the temperature, and the volume of the aqueous solution. Time course experiments were then performed for different initial enzyme concentrations (0.5, 0.9, and 1.4 U_H/mL of solvent). The optimized reaction conditions found were 20 mg of Lipozyme (0.9 U_H/mL_solvent) and 5.0 mL of Na₂CO_3(sat) at 40°C for 6 h.     

NMR Conformational Analysis and Theoretical Calculations for 2‐Aryl‐ 1,3‐dihydroxy‐4,4,5,5‐tetramethylimidazolidines

Conformational studies of 1,3‐dihydroxy‐4,4,5,5‐tetramethyl‐2‐(pyridin‐1‐yl)imidazolidine ( 1a ) and 1,3‐dihydroxy‐4,4,5,5‐tetramethyl‐2‐(pyridin‐3‐yl)imidazolidine ( 1b ), carried out by using 1D ¹H‐ and ¹³C‐NMR and 2D HMQC, HMBC, and NOESY experiments and with the aid of theoretical calculations, indicate that the OH groups are trans to the pyridinyl substituent. Because the two ¹H‐NMR signals of the Me groups are distinguishable and do not change between 290 and 380 K, it is proposed that 1a and 1b have each only one conformation in this temperature range. This behavior was not found with 1,3‐dihydroxy‐4,4,5,5‐tetramethyl‐2‐(pyridin‐2‐yl)imidazolidine ( 1c ) because its Me ¹H‐NMR signals cross over at 300 K. Hence, more than one conformation must be present, beyond those produced by simple inversions. Theoretical calculations including temperature and solvent effects were performed to provide further information on the conformational analysis and to help to assign the NMR data. The combination of NMR measurements and quantum‐chemical calculations is shown to be a very promising strategy for conformational analysis studies in solution.     

Latex Fractionation by Sedimentation and Colloidal Crystallization: The Case of Poly(styrene-co-acrylamide)

Poly(styrene-co-acrylamide) (PS-AAM) latex was prepared, fractionated by sedimentation under gravity, and characterized by PCS, infrared spectra, secondary and backscattered electron imaging in the scanning electron microscope, and electron spectroscopy imaging in an analytical transmission electron microscope. Three latex fractions were obtained. The lower fraction was opalescent and its particles were the more uniform, concerning size, chemical composition, and topochemical features. This lower fraction was still further fractionated by zonal centrifugation in a density gradient, yielding two fractions with similar macrocrystal-forming abilities but different sizes and chemical compositions. These results confirm those previously obtained for the PS-HEMA latex. Copyright 2000 Academic Press.     

Ruthenium(III)- and osmium(VIII)-catalyzed oxidation of 2-thiouracil by bromamine-B in acid and alkaline media: a kinetic and mechanistic study

The kinetics of oxidation of 2-thiouracil (TU) by sodium N-bromobenzenesulphonamide or bromamine-B (BAB) have been studied in an HCl medium, catalyzed by RuCl₃, and in a NaOH media with OsO₄ as catalyst, at 313 K. The stoichiometry and oxidation products are the same in both cases, but their kinetic patterns were found to be different. In acid medium the rate shows a first order dependence in each of [BAB] and [TU], and is dependent on [Ru^III]. The reaction rate is inversely dependent on [H⁺]. In alkaline medium, the rate is first order in [BAB] and in [Os^VIII] and zero order in [TU]. The reaction rate is dependent on [NaOH]. Activation parameters have been evaluated, solvent isotope effects have been studied in D₂O medium, and equilibrium constants were calculated. The activation parameters and rate constants indicate that the catalytic efficiency is: Os^VIII > Ru^III. The proposed mechanisms and the derived rate laws are consistent with the observed kinetics.