83 research outputs found
Gravitational magnetic monopoles and Majumdar-Papapetrou stars
A large amount of work has been dedicated to studying general relativity
coupled to non-Abelian Yang-Mills type theories. It has been shown that the
magnetic monopole, a solution of the Yang-Mills-Higgs equations can be coupled
to gravitation. For a low Higgs mass there are regular solutions, and for a
sufficiently massive monopole the system develops an extremal magnetic
Reissner-Nordstrom quasi-horizon. These solutions, called quasi-black holes,
although non-singular, are arbitrarily close to having a horizon. However, at
the critical value the quasi-black hole turns into a degenerate spacetime. On
the other hand, for a high Higgs mass, a sufficiently massive monopole develops
also a quasi-black hole, but it turns into an extremal true horizon, with
matter fields outside. One can also put a small Schwarzschild black hole inside
the magnetic monopole, an example of a non-Abelian black hole. Surprisingly,
Majumdar-Papapetrou systems, Abelian systems constructed from extremal dust,
also show a resembling behavior. Previously, we have reported that one can find
Majumdar-Papapetrou solutions which can be arbitrarily close of being a black
hole, displaying quasi-black hole behavior. With the aim of better
understanding the similarities between gravitational monopoles and
Majumdar-Papapetrou systems, we study a system composed of two extremal
electrically charged spherical shells (or stars, generically) in the
Einstein--Maxwell--Majumdar-Papapetrou theory. We review the gravitational
properties of the monopoles, and compare with the properties of the double
extremal electric shell system. These quasi-black holes can help in the
understanding of true black holes, and can give insight into the nature of the
entropy of black holes in the form of entanglement.Comment: 38 pages,9 Figures, minor change
Quasinormal modes of black holes in anti-de Sitter space: a numerical study of the eikonal limit
Using series solutions and time-domain evolutions, we probe the eikonal limit
of the gravitational and scalar-field quasinormal modes of large black holes
and black branes in anti-de Sitter backgrounds. These results are particularly
relevant for the AdS/CFT correspondence, since the eikonal regime is
characterized by the existence of long-lived modes which (presumably) dominate
the decay timescale of the perturbations. We confirm all the main qualitative
features of these slowly-damped modes as predicted by Festuccia and Liu
(arXiv:0811.1033) for the scalar-field (tensor-type gravitational)
fluctuations. However, quantitatively we find dimensional-dependent correction
factors. We also investigate the dependence of the QNM frequencies on the
horizon radius of the black hole (brane) and the angular momentum (wavenumber)
of vector- and scalar-type gravitational perturbations.Comment: 5 pages, RevTex4. v2: References added and minor typos corrected.
Published versio
Quasinormal modes of plane-symmetric anti-de Sitter black holes: a complete analysis of the gravitational perturbations
We study in detail the quasinormal modes of linear gravitational
perturbations of plane-symmetric anti-de Sitter black holes. The wave equations
are obtained by means of the Newman-Penrose formalism and the Chandrasekhar
transformation theory. We show that oscillatory modes decay exponentially with
time such that these black holes are stable against gravitational
perturbations. Our numerical results show that in the large (small) black hole
regime the frequencies of the ordinary quasinormal modes are proportional to
the horizon radius (wave number ). The frequency of the purely
damped mode is very close to the algebraically special frequency in the small
horizon limit, and goes as in the opposite limit. This result
is confirmed by an analytical method based on the power series expansion of the
frequency in terms of the horizon radius. The same procedure applied to the
Schwarzschild anti-de Sitter spacetime proves that the purely damped frequency
goes as , where is the quantum number characterizing
the angular distribution. Finally, we study the limit of high overtones and
find that the frequencies become evenly spaced in this regime. The spacing of
the frequency per unit horizon radius seems to be a universal quantity, in the
sense that it is independent of the wave number, perturbation parity and black
hole size.Comment: Added new material on the asymptotic behavior of QNM
Quasiblack holes with pressure: relativistic charged spheres as the frozen stars
In general relativity coupled to Maxwell's electromagnetism and charged
matter, when the gravitational potential and the electric potential field
obey a relation of the form , where , and are arbitrary constants, and (the
speed of light and Newton's constant are put to one), a class of very
interesting electrically charged systems with pressure arises. We call the
relation above between and , the Weyl-Guilfoyle relation, and it
generalizes the usual Weyl relation, for which . For both, Weyl and
Weyl-Guilfoyle relations, the electrically charged fluid, if present, may have
nonzero pressure. Fluids obeying the Weyl-Guilfoyle relation are called
Weyl-Guilfoyle fluids. These fluids, under the assumption of spherical
symmetry, exhibit solutions which can be matched to the electrovacuum
Reissner-Nordstr\"om spacetime to yield global asymptotically flat cold charged
stars. We show that a particular spherically symmetric class of stars found by
Guilfoyle has a well-behaved limit which corresponds to an extremal
Reissner-Nordstr\"om quasiblack hole with pressure, i.e., in which the fluid
inside the quasihorizon has electric charge and pressure, and the geometry
outside the quasihorizon is given by the extremal Reissner-Nordstr\"om metric.
The main physical properties of such charged stars and quasiblack holes with
pressure are analyzed. An important development provided by these stars and
quasiblack holes is that without pressure the solutions, Majumdar-Papapetrou
solutions, are unstable to kinetic perturbations. Solutions with pressure may
avoid this instability. If stable, these cold quasiblack holes with pressure,
i.e., these compact relativistic charged spheres, are really frozen stars.Comment: 16 pages, 8 figures; minor change
Geodesic stability, Lyapunov exponents and quasinormal modes
Geodesic motion determines important features of spacetimes. Null unstable
geodesics are closely related to the appearance of compact objects to external
observers and have been associated with the characteristic modes of black
holes. By computing the Lyapunov exponent, which is the inverse of the
instability timescale associated with this geodesic motion, we show that, in
the eikonal limit, quasinormal modes of black holes in any dimensions are
determined by the parameters of the circular null geodesics. This result is
independent of the field equations and only assumes a stationary, spherically
symmetric and asymptotically flat line element, but it does not seem to be
easily extendable to anti-de Sitter spacetimes. We further show that (i) in
spacetime dimensions greater than four, equatorial circular timelike geodesics
in a Myers-Perry black hole background are unstable, and (ii) the instability
timescale of equatorial null geodesics in Myers-Perry spacetimes has a local
minimum for spacetimes of dimension d > 5.Comment: 13 pages, 2 Figs, RevTex4. v2: Minor corrections. v3: more minor
correction
A class of exact solutions of Einstein's field equations in higher dimensional spacetimes, d: Majumdar-Papapetrou solutions
The Newtonian theory of gravitation and electrostatics admit equilibrium
configurations of charged fluids where the charge density can be equal to the
mass density, in appropriate units. The general relativistic analog for charged
dust stars was discovered by Majumdar and by Papapetrou. In the present work we
consider Einstein-Maxwell solutions in d-dimensional spacetimes and show that
there are Majumdar-Papapetrou type solutions for all . It is
verified that the equilibrium is independent of the shape of the distribution
of the charged matter. It is also showed that for perfect fluid solutions
satisfying the Majumdar-Papapetrou condition with a boundary where the pressure
is zero, the pressure vanishes everywhere, and that the -dimensional spatial section of the spacetime is conformal to a
Ricci-flat space. The Weyl d-dimensional axisymmetric solutions are generalized
to include electric field and charged matter.Comment: 26 pages, no figure
O USO DO FEEDBACK AUTOMÁTICO NO APLICATIVO EDUCACIONAL BUSUU E SUA INFLUÊNCIA NA APRENDIZAGEM DE LÍNGUAS
A tecnologia permeia a aprendizagem de línguas há muitos anos e de várias formas. É o caso do aplicativo Busuu, que possibilita a aprendizagem de 12 idiomas, colaborativa e gratuitamente, contando com 4 milhões de usuários no Brasil. Percebendo esse alcance do Busuu, observamos como se constitui o seu feedback automático, pois essa é sua principal forma de interação com o usuário, sendo essencial no processo de aquisição de uma LE. A base para a análise são as categorias de feedback de Leffa (2003) para AVAs, que são: genérico, situado e estratégico. Realizamos todos os modelos de tarefas do aplicativo em busca das formas de feedback que ele disponibiliza e de como o usuário as recebe. Constatamos que o feedback mais utilizado é o genérico, que pouco proporciona estratégias de aprendizagem e, em menor proporção, o feedback situado, o qual oferece dicas ao usuário para ajudá-lo a chegar na resposta correta
- …