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Quasinormal modes, strong cosmic censorship and instabilities
No full textQuasinormal
modes (QNMs) are the damped vibrations of black hole (BH) spacetimes,
characterising much of the response of a black hole to perturbations. In
Chapter 1, we introduce quasinormal modes, their applications, and ways
to compute them numerically using pseudospectral methods.In
Chapter 2 we study the scalar QNM spectrum of Kerr-Newman. Starting from
the Reissner-Nordström limit, we understand how the spectrum changes as
we vary the ratio of charge to angular momentum, all the way until the
Kerr limit. This clarifies the relationship between the QNM spectra of
Reissner-Nordström and Kerr, and highlights an intricate form of
interaction called eigenvalue repulsion.In asymptotically de
Sitter (dS) spacetimes, an important application of quasinormal modes is
the strong cosmic censorship (SCC) conjecture. In four dimensions,
Christodoulou's formulation of SCC is violated by charged BHs
(Reissner-Nordström-dS), but holds for rotating BHs (Kerr-dS). In
Chapter 3, we study a higher-dimensional analogue of Kerr-dS, equal
angular momentum Myers-Perry-dS, and show that SCC is respected in odd d
>= 5 dimensions. This suggests that the preservation of SCC in
uncharged rotating black hole backgrounds might be a universal property
of Einstein gravity and not limited to the d = 4 Kerr-dS background.Finally,
in Chapter 4, we construct the static hairy black holes of
Einstein-Maxwell-Scalar theory in a cavity that confines the scalar
field. These hairy black holes are asymptotically flat, with a scalar
condensate floating above the horizon. When they coexist with
Reissner-Nordström BHs, the hairy BHs are thermodynamically preferred,
and hence they are natural candidates for the endpoint of the
superradiant and near-horizon instabilities of the charged black hole
bomb system.</p
Fully constrained, high-resolution shock-capturing, formulation of the Einstein-fluid equations in 2+1 dimensions
No full textFour components of the axisymmetric Einstein equations in 2+1 dimensions with negative cosmological constant can be written as aM=... and aJ=..., where the dots stand for stress-energy terms, and M and J are scalars. In vacuum, they reduce to the constant mass and angular momentum parameters of the BTZ solution of the same name. The integrability conditions for the Einstein equations give rise to two conserved stress-energy currents aj(M)a=0 and aj(J)a=0. The angular momentum current is just the Noether current due to axisymmetry, but the mass current is unexpected in the presence of rotation. The conserved quantity M exists in all dimensions in spherical symmetry, known as the Misner-Sharp, Hawking or Kodama mass, but in 2+1 dimensions M exists also in axisymmetry, even with rotation. We use M and J to give a fully constrained formulation of the axisymmetric Einstein equations in 2+1 dimensions, where the Einstein equations are solved by explicit integration from the center along time slices. We use the two conserved matter currents in the construction of a high-resolution shock-capturing formulation of the Einstein-perfect fluid system, in which M and J momentum are then exactly conserved by construction. We demonstrate convergence of the code in the test cases of generic dispersion and collapse and stable and unstable rotating stars.</p
Strong cosmic censorship in Kerr-Newman-de Sitter
No full textChristodoulou’s formulation of Strong Cosmic Censorship (SCC) holds true for Kerr-de Sitter black holes. On the other hand, Reissner-Nordström-de Sitter black holes violate SCC. We do a detailed scan of the parameter space of Kerr-Newman-de Sitter black holes between these two limiting families, to identify the boundary that marks the transition between solutions that respect and violate SCC. We focus our attention on linear scalar field perturbations. SCC is violated inside a (roughly) ‘spherical’ shell of the parameter space of Kerr-Newman-de Sitter, centred at the corner that describes arbitrarily small extremal Reissner-Nordström-de Sitter solutions. Outside of this region, including the Kerr-de Sitter limit, we identify perturbation modes that decay slow enough to enforce SCC. Additionally, we do a necessary study of the quasinormal mode spectra of Kerr-Newman-de Sitter in some detail. As established in the literature, in the Kerr-de Sitter and Reissner-Nordström-de Sitter limits, we find three families of modes: de Sitter, photon sphere and near-horizon modes. These interact non-trivially away from the Reissner-Nordström-de Sitter limit and display eigenvalue repulsions like in Kerr-Newman black holes.</p
Phase diagram of the charged black hole bomb system
Full text linkWe find the phase diagram of solutions of the charged black hole bomb system.
In particular, we find the static hairy black holes of Einstein-Maxwell-Scalar
theory confined in a Minkowski box. We impose boundary conditions such that the
scalar field vanishes at and outside a cavity of constant radius. These hairy
black holes are asymptotically flat with a scalar condensate floating above the
horizon. We identify four critical scalar charges which mark significant
changes in the qualitative features of the phase diagram. When they coexist,
hairy black holes always have higher entropy than the Reissner-Nordstr\"om
black hole with the same quasilocal mass and charge. So hairy black holes are
natural candidates for the endpoint of the superradiant/near-horizon
instabilities of the black hole bomb system. We also relate hairy black holes
to the boson stars of the theory. When it has a zero horizon radius limit, the
hairy black hole family terminates on the boson star family. Finally, we find
the Israel surface tensor of the box required to confine the scalar condensate
and that it can obey suitable energy conditions.Comment: 36 pages, 12 figure
Scalar QNM spectra of Kerr and Reissner-Nordström revealed by eigenvalue repulsions in Kerr-Newman
No full textRecent studies of the gravito-electromagnetic frequency spectra of Kerr-Newman (KN) black holes have revealed two families of quasinormal modes (QNMs), namely photon sphere modes and near-horizon modes. However, they can only be unambiguously distinguished in the Reissner-Nordström (RN) limit, due to a phenomenon called eigenvalue repulsion (also known as level repulsion, avoided crossing or the Wigner-Teller effect), whereby the two families can interact strongly near extremality. We find that these features are also present in the QNM spectra of a scalar field in KN, where the perturbation modes are described by ODEs and thus easier to explore. Starting from the RN limit, we study how the scalar QNM spectra of KN dramatically changes as we vary the ratio of charge to angular momentum, all the way until the Kerr limit, while staying at a fixed distance from extremality. This scalar field case clarifies the (so far puzzling) relationship between the QNM spectra of RN and Kerr black holes and the nature of the eigenvalue repulsions in KN, that ultimately settle the fate of the QNM spectra in Kerr. We study not just the slowest-decaying QNMs (both for ℓ=m=0 and ℓ=m=2), but several sub-dominant overtones as well, as these turn out to play a crucial role understanding the KN QNM spectra. We also give a new high-order WKB expansion of KN QNMs that typically describes the photon sphere modes beyond the eikonal limit, and use a matched asymptotic expansion to get a very good approximation of the near-horizon modes near extremality
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Strong cosmic censorship and Eigenvalue Repulsions for rotating de Sitter black holes in higher-dimensions
No full textIt has been established that Christodoulou’s formulation of Strong Cosmic Censorship (SCC) is violated by Reissner-Nordström-de Sitter black holes, but holds in four-dimensional Kerr-de Sitter black holes. We show that SCC is also respected by equal angular momenta (cohomogeneity-1) Myers-Perry-de Sitter (MP-dS) in odd d ≥ 5 spacetime dimensions. This suggests that the preservation of SCC in rotating backgrounds might be a universal property of Einstein gravity and not limited to the d = 4 Kerr-dS background. As required to discuss SCC in de Sitter spacetimes, we also study important aspects of the scalar field quasinormal mode (QNM) spectra of MP-dS. In particular, we find eigenvalue repulsions similar to those recently observed in the QNM spectra of asymptotically flat Kerr-Newman black holes. For axisymmetric modes (i.e. with azimuthal quantum number m = 0) there are three distinct families of QNM (de Sitter, photon sphere and near-horizon). However, typically, for non-axisymmetric (m ≠ 0) QNMs, we find that the entire spectra can be described by just two families of QNM (since several overtone sections of the photon sphere and near-horizon families merge). For completeness, we also study the full scalar field QNM spectra of higher-dimensional Schwarzschild-de Sitter black holes
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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