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.