On the interaction between two Kerr black holes

The double-Kerr solution is generated using both a Backlund transformation and the Belinskii-Zakharov inverse-scattering technique. We build a dictionary between the parametrisations naturally obtained in the two methods and show their equivalence. We then focus on the asymptotically flat double-Kerr system obeying the axis condition which is Z_2^\phi invariant; for this system there is an exact formula for the force between the two black holes, in terms of their physical quantities and the coordinate distance. We then show that 1) the angular velocity of the two black holes decreases from the usual Kerr value at infinite distance to zero in the touching limit; 2) the extremal limit of the two black holes is given by |J|=cM^2, where c depends on the distance and varies from one to infinity as the distance decreases; 3) for sufficiently large angular momentum the temperature of the black holes attains a maximum at a certain finite coordinate distance. All of these results are interpreted in terms of the dragging effects of the system.Comment: 19 pages, 4 figures. v2: changed statement about thermodynamical equilibrium in section 3; minor changes; added references. v3: added references to previous relevant work; removed one equation (see note added); other minor corrections; final version to be published in JHE

Fibrations of genus two on complex surfaces

We consider fibrations of genus 2 over complex surfaces. The purpose of this paper is primarily to provide a geometric description of the possible structures of the fibration on a neighborhood of a singular fiber. In particular it is shown that the "geometric data" of the singular fiber determines the fibration on its neighborhood up to a transversely holomorphic $C^{\infty}$-diffeomorphism. The method employed is quite flexible and it applies to good extent to fibrations of arbitrary genus.Comment: This is the final version, June 201

Impact of Inter-Country Distances on International Tourism

Tourism is a worldwide practice with international tourism revenues increasing from US\$495 billion in 2000 to US\$1340 billion in 2017. Its relevance to the economy of many countries is obvious. Even though the World Airline Network (WAN) is global and has a peculiar construction, the International Tourism Network (ITN) is very similar to a random network and barely global in its reach. To understand the impact of global distances on local flows, we map the flow of tourists around the world onto a complex network and study its topological and dynamical balance. We find that although the WAN serves as infrastructural support for the ITN, the flow of tourism does not correlate strongly with the extent of flight connections worldwide. Instead, unidirectional flows appear locally forming communities that shed light on global travelling behaviour inasmuch as there is only a 15% probability of finding bidirectional tourism between a pair of countries. We conjecture that this is a consequence of one-way cyclic tourism by analyzing the triangles that are formed by the network of flows in the ITN. Finally, we find that most tourists travel to neighbouring countries and mainly cover larger distances when there is a direct flight, irrespective of the time it takes

On the backreaction of frame dragging

The backreaction on black holes due to dragging heavy, rather than test, objects is discussed. As a case study, a regular black Saturn system where the central black hole has vanishing intrinsic angular momentum, J^{BH}=0, is considered. It is shown that there is a correlation between the sign of two response functions. One is interpreted as a moment of inertia of the black ring in the black Saturn system. The other measures the variation of the black ring horizon angular velocity with the central black hole mass, for fixed ring mass and angular momentum. The two different phases defined by these response functions collapse, for small central black hole mass, to the thin and fat ring phases. In the fat phase, the zero area limit of the black Saturn ring has reduced spin j^2>1, which is related to the behaviour of the ring angular velocity. Using the `gravitomagnetic clock effect', for which a universality property is exhibited, it is shown that frame dragging measured by an asymptotic observer decreases, in both phases, when the central black hole mass increases, for fixed ring mass and angular momentum. A close parallelism between the results for the fat phase and those obtained recently for the double Kerr solution is drawn, considering also a regular black Saturn system with J^{BH}\neq 0.Comment: 18 pages, 8 figure

The use of Similarity Structure Analysis in the identification of students’ functional profiles of competence

This study aims to identify students’ functional profiles - describing the representational functions available to consolidate certain school competences, in a sample of 670 students of Portuguese Basic Schools, in which 58,3% were girls and 41,7% were boys (33,6% from 1st level, 36,0% from 2nd level and 30,4% from 3rd level). Four instruments were used: Questionnaire of the Attitudes Towards School, Questionnaire of the Attitudes Towards Portuguese Language, Questionnaire of the Attitudes Towards Mathematics and EQi-yv. Based on the SSA the polar structure observed, combined with the relative position of the external variable, it is possible to suggest the existence of differentiated profiles considering personal and scholarly features that become more efficient with school progress, pointing out the necessity to consider these variables independently when school policy decisions are taken. The advantages of these techniques to improve the characterization and interpretation of the complexity and multidimensionality of students´ profiles and their consequences for educational and psychological assessment and intervention are discussed

Atitudes face à Língua Portuguesa e Matemática em alunos de altas habilidades

As atitudes face às matérias de ensino constituem um importante preditor de sucesso educativo, combinando componentes afetivas, instrumentais e comportamentais que podem mediar o processo e os resultados da aprendizagem (Rebelo, 2012; Roazzi, Diniz, & Candeias, no prelo). Atendendo à especificidade do grupo de alunos com altas habilidades e à sua vulnerabilidade em termos de rendimento escolar, propomos compreender as atitudes face às disciplinas de língua portuguesa (LP) e matemática (Mat.) nestes alunos e alunas, no âmbito de um projeto mais amplo cuja finalidade é perceber a relação entre Rendimento Escolar e Desenvolvimento de alunos do Ensino Básico (RED)