Abstract:
Finding the origin of Hawking radiation has been a puzzle to researchers. Using a loop quantum gravity description of a black hole slice, a density matrix is defined using coherent states for space-times with apparent horizons. Evolving the density matrix using a semi-classical Hamiltonian in the frame of an observer outside the horizon gives the origin of Hawking radiation.

Abstract:
We present a general result giving us families of incomplete and boundedly complete families of discrete distributions. For such families, the classes of unbiased estimators of zero with finite variance and of parametric functions which will have uniformly minimum variance unbiased estimators with finite variance are explicitly characterized. The general result allows us to construct a large number of families of incomplete and boundedly complete families of discrete distributions. Several new examples of such families are described.

Abstract:
The nickel-resistant bacterium, Cupriavidus pauculus KPS 201 was isolated from the rhizosphere of Rinorea bengalensis (Wall.) O. K. endemic to metal-percolated ultramafic ecosystem of Andaman, India. This study investigates nature of Ni resistance, growth associated uptake and localization of Ni in cellular compartments of KPS 201. Growth kinetics of C. pauculus KPS 201 exhibited a typical inducible Ni resistance in Ni-supplemented (1.0-10.0 mM) Tris-minimal medium. The Ni-induced cells showed a high degree of Ni resistance and accumulated a maximum of 29.3 µM Ni/g protein after 48 h of growth in 5 mM Ni. The accumulated Ni was preferentially retained (90.6%) in the periplasm and was associated with the expression of two periplasmic proteins (74 and 66 kDa) under Ni-induced condition. Inducible nickel resistance in C. pauculus KPS 201 may possibly be due to extracytoplasmic binding and accumulation coupled with expression of specific periplasmic proteins. These findings will provide an insight in understanding metal-microbe interaction in geogenous environments and their exploitation in bioremediation of heavy metal pollutants.

Abstract:
In this article we explore the origin of black hole thermodynamics using semiclassical states in loop quantum gravity. We re-examine the case of entropy using a density matrix for a coherent state and describe correlations across the horizon due to SU(2) intertwiners. We further show that Hawking radiation is a consequence of a non-Hermitian term in the evolution operator, which is necessary for entropy production or depletion at the horizon. This non-unitary evolution is also rooted in formulations of irreversible physics.

Abstract:
The entropy of apparent horizons is derived using coherent states or semiclassical states in quantum gravity. The leading term is proportional to area for large horizons, and the correction terms differ according to the details of the graph which is used to regularise the quantum gravity phase space variables.

Abstract:
I give a resolution of the conformal mode divergence in the Euclidean gravitational path-integral by isolating the trace of the diffeomorphisms and its contribution to the Faddeev-Popov measure.

Abstract:
In this article a description is given of the measure in Euclidean path-integral in quantum gravity, and recent results using the Faddeev-Popov method of gauge fixing. The results suggest that the effective action is finite and positive.

Abstract:
The emission rate of fermions from 2+1 dimensional BTZ black holes is shown to have a form which can be reproduced from a conformal field theory at finite temperature. The rate obtained for fermions is identical to the rate of non-minimally coupled fermions emitted from a five dimensional black hole, whose near horizon geometry is BTZ X M, where M is a compact manifold.