Inextendible Schwarzschild black hole with a single exterior: How thermal is the Hawking radiation?

Several approaches to Hawking radiation on Schwarzschild spacetime rely in some way or another on the fact that the Kruskal manifold has two causally disconnected exterior regions. We investigate the Hawking(-Unruh) effect for a real scalar field on the \RPthree geon: an inextendible, globally hyperbolic, space and time orientable eternal black hole spacetime that is locally isometric to Kruskal but contains only one exterior region. The Hartle-Hawking-like vacuum~\hhvacgeon, which can be characterized alternatively by the positive frequency properties along the horizons or by the complex analytic properties of the Feynman propagator, turns out to contain exterior region Boulware modes in correlated pairs, and any operator in the exterior that only couples to one member of each correlated Boulware pair has thermal expectation values in the usual Hawking temperature. Generic operators in the exterior do not have this special form; however, we use a Bogoliubov transformation, a particle detector analysis, and a particle emission-absorption analysis that invokes the analytic properties of the Feynman propagator, to argue that \hhvacgeon appears as a thermal bath with the standard Hawking temperature to any exterior observer at asymptotically early and late Schwarzschild times. A~(naive) saddle-point estimate for the path-integral-approach partition function yields for the geon only half of the Bekenstein-Hawking entropy of a Schwarzschild black hole with the same ADM mass: possible implications of this result for the validity of path-integral methods or for the statistical interpretation of black-hole entropy are discussed. Analogous results hold for a Rindler observer in a flat spacetime whose global properties mimic those of the geon.Comment: 53 pages, REVTex v3.1 with amsfonts and epsf, includes 5 eps figures. (v2: Title and abstract expanded, minor comments added. v3: Minor typos corrected.

MI as a predictor of students’ performance in reading competency

The purpose of this study was to examine whether performance in MI could predict the performance in reading competency. The other objectives were to identify the components of MI which are correlated with the reading test scores, and to determine the relationship between the multiple intelligences and reading proficiency. A descriptive and ex post facto design was employed to ascertain relationships among the variables. The participants were 128 randomly chosen pre-university students (grade12, 18-19 years old) of both genders studying in Tehran in the academic year 2008-2009. Three instruments were utilized in this study: 1) a demographic questionnaire; 2) the Persian version of Mckenzie’s MI Inventory; and 3) a standardized reading proficiency test which was selected from retrieved paper-based TOEFL® tests. Results of the correlation analysis revealed no significant relationship between the two variables of MI and reading scores of the students. Furthermore, the results of the correlation analysis revealed that there was a low significant, negative relationship between musical-rhythmic intelligence and reading which suggests that when the reading score of a student increases, musical-rhythmic intelligence of the same student decreases and vice versa. Overall, three categories of MI (musical-rhythmic, verbal-linguistic, bodily-kinesthetic) were found to be predictive of reading proficiency

ON THE PRODUCT AND RATIO OF PARETO AND KUMARASWAMY RANDOM VARIABLES

The distributions of the product XY and the ratio X/Y are derivedwhen X and Y are Pareto and the Kumaraswamy random variablesdistributed independently of each other