Thermodynamics of black branes in asymptotically Lifshitz spacetimes

Recently, a class of gravitational backgrounds in 3+1 dimensions have been proposed as holographic duals to a Lifshitz theory describing critical phenomena in 2+1 dimensions with critical exponent $z\geq 1$. We continue our earlier work \cite{Bertoldi:2009vn}, exploring the thermodynamic properties of the "black brane" solutions with horizon topology $\mathbb{R}^2$. We find that the black branes satisfy the relation $\mathcal{E}=\frac{2}{2+z}Ts$ where $\mathcal{E}$ is the energy density, $T$ is the temperature, and $s$ is the entropy density. This matches the expected behavior for a 2+1 dimensional theory with a scaling symmetry $(x_1,x_2)\to \lambda (x_1,x_2)$, $t\to \lambda^z t$.Comment: 8 pages, references added and regroupe

Hawking Radiation from Feynman Diagrams

The aim of this letter is to clarify the relationships between Hawking radiation and the scattering of light by matter falling into a black hole. To this end we analyze the S-matrix elements of a model composed of a massive infalling particle (described by a quantized field) and the radiation field. These fields are coupled by current-current interactions and propagate in the Schwarzschild geometry. As long as the photons energy is much smaller than the mass of the infalling particle, one recovers Hawking radiation since our S-matrix elements identically reproduce the Bogoliubov coefficients obtained by treating the trajectory of the infalling particle classically. But after a brief period, the energy of the `partners' of Hawking photons reaches this mass and the production of thermal photons through these interactions stops. The implications of this result are discussed.Comment: 12 pages, revtex, no figure

Dilaton Black Holes Near the Horizon

Generic $U(1)^2$ 4-d black holes with unbroken $N=1$ supersymmetry are shown to tend to a Robinson-Bertotti type geometry with a linear dilaton and doubling of unbroken supersymmetries near the horizon. Purely magnetic dilatonic black holes, which have unbroken $N=2$ supersymmetry, behave near the horizon as a 2-d linear dilaton vacuum $\otimes \, S^2$. This geometry is invariant under 8 supersymmetries, i.e. half of the original $N=4$ supersymmetries are unbroken. The supersymmetric positivity bound, which requires the mass of the 4-d dilaton black holes to be greater than or equal to the central charge, corresponds to positivity of mass for a class of stringy 2-d black holes.Comment: 10 pages, SU-ITP-92-2

Original Article

The development of cognitive and socioemotional skills early in life influences later health and well-being. Existing estimates of unmet developmental potential in low- and middle-income countries (LMICs) are based on either measures of physical growth or proxy measures such as poverty. In this paper we aim to directly estimate the number of children in LMICs who would be reported by their caregivers to show low cognitive and/or socioemotional development.The present paper uses Early Childhood Development Index (ECDI) data collected between 2005 and 2015 from 99,222 3- and 4-y-old children living in 35 LMICs as part of the Multiple Indicator Cluster Survey (MICS) and Demographic and Health Surveys (DHS) programs. First, we estimate the prevalence of low cognitive and/or socioemotional ECDI scores within our MICS/DHS sample. Next, we test a series of ordinary least squares regression models predicting low ECDI scores across our MICS/DHS sample countries based on country-level data from the Human Development Index (HDI) and the Nutrition Impact Model Study. We use cross-validation to select the model with the best predictive validity. We then apply this model to all LMICs to generate country-level estimates of the prevalence of low ECDI scores globally, as well as confidence intervals around these estimates. In the pooled MICS and DHS sample, 14.6% of children had low ECDI scores in the cognitive domain, 26.2% had low socioemotional scores, and 36.8% performed poorly in either or both domains. Country-level prevalence of low cognitive and/or socioemotional scores on the ECDI was best represented by a model using the HDI as a predictor. Applying this model to all LMICs, we estimate that 80.8 million children ages 3 and 4 y (95% CI 48.1 million, 113.6 million) in LMICs experienced low cognitive and/or socioemotional development in 2010, with the largest number of affected children in sub-Saharan Africa (29.4.1 million; 43.8% of children ages 3 and 4 y), followed by South Asia (27.7 million; 37.7%) and the East Asia and Pacific region (15.1 million; 25.9%). Positive associations were found between low development scores and stunting, poverty, male sex, rural residence, and lack of cognitive stimulation. Additional research using more detailed developmental assessments across a larger number of LMICs is needed to address the limitations of the present study.The number of children globally failing to reach their developmental potential remains large. Additional research is needed to identify the specific causes of poor developmental outcomes in diverse settings, as well as potential context-specific interventions that might promote children's early cognitive and socioemotional well-being

Extremal Black Holes As Fundamental Strings

We show that polarization dependent string-string scattering provides new evidence for the identification of the Dabholkar-Harvey (DH) string solution with the heterotic string itself. First, we construct excited versions of the DH solution which carry arbitrary left-moving waves yet are annihilated by half the supersymmetries. These solutions correspond in a natural way to Bogomolny-bound-saturating excitations of the ground state of the heterotic string. When the excited string solutions are compactified to four dimensions, they reduce to Sen's family of extremal black hole solutions of the toroidally compactified heterotic string. We then study the large impact parameter scattering of two such string solutions. We develop methods which go beyond the metric on moduli space approximation and allow us to read off the subleading polarization dependent scattering amplitudes. We find perfect agreement with heterotic string tree amplitude predictions for the scattering of corresponding string states. Taken together, these results clearly identify the string states responsible for Sen's extremal black hole entropy. We end with a brief discussion of implications for the black hole information problem.Comment: 38 pages, 1 encapsulated postscript figure, uses harvmac.tex and epsf.te

Early Childhood Development and Schooling Attainment: Longitudinal Evidence from British, Finnish and Philippine Birth Cohorts

Background While recent literature has highlighted the importance of early childhood development for later life outcomes, comparatively little is known regarding the relative importance of early physical and cognitive development in predicting educational attainment cross-culturally. Methods We used prospective data from three birth cohorts: the Northern Finland Birth Cohort of 1986 (NFBC1986), the 1970 British Cohort Study (BCS1970), and the Cebu Longitudinal Health and Nutrition Survey of 1983 (CLHNS) to assess the association of height-for-age z-score (HAZ) and cognitive development measured prior to age 8 with schooling attainment. Multivariate linear regression models were used to estimate baseline and adjusted associations. Results Both physical and cognitive development were highly predictive of adult educational attainment conditional on parental characteristics. The largest positive associations between physical development and schooling were found in the CLHNS (β = 0.53, 95%-CI: [0.32, 0.74]) with substantially smaller associations in the BCS1970 (β = 0.10, 95% CI [0.04, 0.16]) and the NFBC1986 (β = 0.06, 95% CI [-0.05, 0.16]). Strong associations between cognitive development and educational attainment were found for all three cohorts (NFBC1986: β = 0.22, 95%-CI: [0.12, 0.31], BCS1970: β = 0.58, 95%-CI: [0.52, 0.64], CLHNS: β = 1.08, 95%-CI: [0.88, 1.27]). Models jointly estimating educational associations of physical and cognitive development demonstrated weaker associations for physical development and minimal changes for cognitive development. Conclusion The results indicate that although physical and cognitive early development are both important predictors of educational attainment, cognitive development appears to play a particularly important role. The large degree of heterogeneity in the observed effect sizes suggest that the importance of early life physical growth and cognitive development is highly dependent on socioeconomic and institutional contexts