Energy Conservation and Hawking Radiation

The conservation of energy implies that an isolated radiating black hole cannot have an emission spectrum that is precisely thermal. Moreover, the no-hair theorem is only approximately applicable. We consider the implications for the black hole information puzzle.Comment: 6 pages, LaTex; v2: references adde

The Volume of Black Holes

We propose a definition of volume for stationary spacetimes. The proposed volume is independent of the choice of stationary time-slicing, and applies even though the Killing vector may not be globally timelike. Moreover, it is constant in time, as well as simple: the volume of a spherical black hole in four dimensions turns out to be just ${4 \over 3} \pi r_+^3$. We then consider whether it is possible to construct spacetimes that have finite horizon area but infinite volume, by sending the radius to infinity while making discrete identifications to preserve the horizon area. We show that, in three or four dimensions, no such solutions exist that are not inconsistent in some way. We discuss the implications for the interpretation of the Bekenstein-Hawking entropy.Comment: 8 pages, revte

De Sitter Space With Finitely Many States: A Toy Story

The finite entropy of de Sitter space suggests that in a theory of quantum gravity there are only finitely many states. It has been argued that in this case there is no action of the de Sitter group consistent with unitarity. In this note we propose a way out of this if we give up the requirement of having a hermitian Hamiltonian. We argue that some of the generators of the de Sitter group act in a novel way, namely by mixing in- and out-states. In this way it is possible to have a unitary S-matrix that is finite-dimensional and, moreover, de Sitter-invariant. Using Dirac spinors, we construct a simple toy model that exhibits these features.Comment: 6 pages, LaTe

Smooth Initial Conditions from Weak Gravity

CMB measurements reveal an unnaturally smooth early universe. We propose a mechanism to make this smoothness natural by weakening the strength of gravity at early times, and therefore altering which initial conditions have low entropy.Comment: 14 pages, 5 figures. Minor changes, version appearing in PL

A Beneficiation Scheme for Reduction of Alumina in Iron Ores from Barsua

In order to improve blast furnace productivity by reducing the alumina of iron ore fines from the present level of 3.3-3.9% to the desired level of 2.5%, a detailed characterisation followed by beneficiation studies compris-ing crushing, dry screening, washing, gravity separation of fines and slimes, on the seven individual 'type' and a 'composite' iron ore samples from Barsua Iron Mines were carried out at NML, Jamshedpur to find the amenability of beneficiation and develop a flow-sheet. Based on the find-ings from the studies, two conceptual flowsheets were designed.The first one consisted of crushing the composite sample (62.26% Fe, 2.01% Si02 and 4.22% A1203) to 25 mm followed by wet processing comprising scrubbing & wet screening at 8 mm and classification of -8mm fraction into sand (+100#) and slime (-100#). The -8+1 mm fraction of the sand would be subjected to jigging and -1mm+100 # fraction to tabling. The cyclone underflow obtained by treating the slime would be subjected to tabling as well. The yield of the combined concentrate of fines would be 28% and analyse 64.09% Fe, 1.9% Si02 and 2.95% A1203. The +8 mm lumps, 45% by weight would analyse 63.69% Fe, 1.52% Si02 and 3.8% A1203. Based on mainly grade and physical characteristics of individual type samples, the Second Flowsheet consists of separate proportioning, blending and treatment of two group of ores viz., Direct Ore (Friable, Mineable Transi-tional and Blue Dust) and Beneficiable Ore (Soft Lamina-ted , Lateritic , Hard Laminated and Massive). The flow-sheet consists of dry processing of Direct Ore (29% by weight with 63.55% Fe, 1.69% Si02 and 2.45% A1203) and wet processing of Beneficiable Ore (71% by weight with 61.39% Fe, 2.22% Si02 and 5.09% A1203). The Dry Circuit would consist of crushing the Direct to -25 mm and screening at 8 mm. The lumps and fines would weigh 8% and 21% and analyse 62.62% Fe, 1.79% Si02 and 2.92% A1203 and 63.9% Fe, 1.65% SiO2 and 2.27% Al2O3 respectively. The Benefic-iable will go through the wet circuit as described for the first flowsheet. The washed lump would be 36.43% by weight and analyse 63.4% Fe, 1.38% Si02 and 4.05% Al2O3. The combined lumps from Dry Circuit and Wet Circuit would be 44.43% by weight and analyse 63.25% Fe, 1.45% Si02 and 3.85% A1203.The combined fines from Dry Circuit and Wet Circuit (without concentrates from slime) would weigh 35.62% and analyse 64.1% Fe, 1.59% Si02 and 2.56% A1203. The yield will improve by an additional amount of 5-6% with slight increase in Al2O3 (2.85%) if table con-centrates from cyclone underflow and overflow are recovered. Although quality or quantity of lumps remain almost same in both the cases, there is substantial improvement in grade and yield of fines in the second flowsheet

Beneficiation of Low Grade Chromite Ores from Sukinda

In order to produce directly marketable chrome ore for export and domestic industries, most of the chromite ore beneficiation plants in Sukinda region treat selected rich ores with rejection of huge quantities of low and sub-grade ore (10-38% Cr2O3). Beneficiation is mostly limited to curshing, grinding, desliming and hydrosizing to prod-uce a concentrate of about 50% Cr203 with a yield of about 25-35%. By this also, a huge amount of sub grade fines of about 35-40% Cr203 has been accumulating in the mines. Currently very little efforts are made to treat these low grade ores or recover values from waste dumps. Recently, a study was undertaken at NML. to explore the possibility of developing a flowsheet to produce chromite concentrate preferably with Cr203 content of about 50% with Si02 about 2% from waste dumps analysing between 20 to 23% Cr203, with a view to using these as additional source of feed stock. Detailed physical characterisation, mineralogical analysis, bench and pilot scale studies were undertaken on these samples. The beneficiation process essentially invo- lved removal of ferruginous slime at stages by washing and hydrocycloning and enrichment of different size classified fractions by. simple gravity separation techniques like spiralling and tabling. It was observed that by adoption of the above operations, it was possible to upgrade these low grade ores to obtain concentrate having Cr203 of desired grade with high recovery

Use of blue dust in sintering

Sintering studies were undertaken through a full factorial design of experi¬ment to estimate the quantitative effect of blue dust along with other process variables. Responses from the experiments were then correlated with the process variables through a regression equation. The coefficients of the equation indicated that the coke breeze exerted maximum influence on the strength. It was possible to incorporate blue dust to the extent of 40% with respect to total iron ore fraction without impairing the properties of sinter