2,181 research outputs found
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
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
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
-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
A Double Myers-Perry Black Hole in Five Dimensions
Using the inverse scattering method we construct a six-parameter family of
exact, stationary, asymptotically flat solutions of the 4+1 dimensional vacuum
Einstein equations, with U(1)^2 rotational symmetry. It describes the
superposition of two Myers-Perry black holes, each with a single angular
momentum parameter, both in the same plane. The black holes live in a
background geometry which is the Euclidean C-metric with an extra flat time
direction. This background possesses conical singularities in two adjacent
compact regions, each corresponding to a set of fixed points of one of the U(1)
actions in the Cartan sub-algebra of SO(4). We discuss several aspects of the
black holes geometry, including the conical singularities arising from force
imbalance, and the torsion singularity arising from torque imbalance. The
double Myers-Perry solution presented herein is considerably simpler than the
four dimensional double Kerr solution and might be of interest in studying
spin-spin interactions in five dimensional general relativity.Comment: 23 pages, 7 figures, LaTeX. v2: minor changes, references added;
version published in JHE
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
Relação entre capacidade intelectual e desempenho a língua portuguesa e matemática
Os alunos com altas capacidades intelectuais sem uma educação escolar apropriada correm o risco de desinvestir na escola.
Contrariamente ao que se pensa, a investigação tem demonstrado que estes alunos, sem o estímulo adequado, correm o risco de
fracassar. Com o objetivo de perceber a relação entre a capacidade intelectual e os resultados escolares (aferidos pelo desempenho a
língua portuguesa (LP) e matemática (Mat.), apresentamos um estudo desenvolvido com alunos portugueses, inserido num projecto
mais amplo cuja finalidade é perceber a relação entre Rendimento Escolar e Desenvolvimento de alunos do Ensino Básico (RED)
- …