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

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

New Coordinates for de Sitter Space and de Sitter Radiation

We introduce a simple coordinate system covering half of de Sitter space. The new coordinates have several attractive properties: the time direction is a Killing vector, the metric is smooth at the horizon, and constant-time slices are just flat Euclidean space. We demonstrate the usefulness of the coordinates by calculating the rate at which particles tunnel across the horizon. When self-gravitation is taken into account, the resulting tunneling rate is only approximately thermal. The effective temperature decreases through the emission of radiation.Comment: LaTeX, 10 pages; v2. references added; v3. minor sign errors fixed, reference added, journal versio

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

Wavelet analysis and scaling properties of time series

We propose a wavelet based method for the characterization of the scaling behavior of non-stationary time series. It makes use of the built-in ability of the wavelets for capturing the trends in a data set, in variable window sizes. Discrete wavelets from the Daubechies family are used to illustrate the efficacy of this procedure. After studying binomial multifractal time series with the present and earlier approaches of detrending for comparison, we analyze the time series of averaged spin density in the 2D Ising model at the critical temperature, along with several experimental data sets possessing multi-fractal behavior.Comment: 4 pages, 4 figures. Accepted for publication in PR

Prevalence of exclusive breastfeeding and its determinants in first 6 months of life: A prospective study

Background: Exclusive breastfeeding for first 6 months of life is recommended under Infant and Young Child Feeding practices in India. The objective of present study was to estimate the prevalence of exclusive breastfeeding during first 6 months of life of babies and to identify factors that interfere with the practice in the study area. Methods: A prospective cohort of 462 women who delivered at maternity unit of Government Medical College & Hospital, Rajkot, which is a tertiary care centre for the district, was studied. Data collection was done at hospital as well as during home visits of babies at 1, 3 and 6 months. Factors related to cessation of breastfeeding were analyzed using univariate, bivariate and multivariate analysis. Results: All 462 mothers reported breastfeeding their newborns. Prevalence of exclusive breastfeeding reported at 3 months was 97% which declined to 62% by 6 months of age of infants. Bivariate analysis revealed no significant association between interruption of exclusive breastfeeding before 6 months of age and various demographic, socioeconomic, maternal and infant characteristics. Multivariate analysis by logistic regression demonstrated no association between discontinuation of exclusive breastfeeding and socioeconomic status, maternal education and maternal age, number of antenatal visits, maternal employment and initiation of breastfeeding after delivery. Conclusion: Exclusive breastfeeding prevalence rate found higher than at national level indicating better feeding practices in these part of India. Also, factors classically considered as supportive for breastfeeding had shown no association with breastfeeding pattern in present study