21 research outputs found
Quasi-Normal Modes of Stars and Black Holes
Perturbations of stars and black holes have been one of the main topics of
relativistic astrophysics for the last few decades. They are of particular
importance today, because of their relevance to gravitational wave astronomy.
In this review we present the theory of quasi-normal modes of compact objects
from both the mathematical and astrophysical points of view. The discussion
includes perturbations of black holes (Schwarzschild, Reissner-Nordstr\"om,
Kerr and Kerr-Newman) and relativistic stars (non-rotating and
slowly-rotating). The properties of the various families of quasi-normal modes
are described, and numerical techniques for calculating quasi-normal modes
reviewed. The successes, as well as the limits, of perturbation theory are
presented, and its role in the emerging era of numerical relativity and
supercomputers is discussed.Comment: 74 pages, 7 figures, Review article for "Living Reviews in
Relativity
The frequency-dependent Wright-Fisher model: diffusive and non-diffusive approximations
We study a class of processes that are akin to the Wright-Fisher model, with
transition probabilities weighted in terms of the frequency-dependent fitness
of the population types. By considering an approximate weak formulation of the
discrete problem, we are able to derive a corresponding continuous weak
formulation for the probability density. Therefore, we obtain a family of
partial differential equations (PDE) for the evolution of the probability
density, and which will be an approximation of the discrete process in the
joint large population, small time-steps and weak selection limit. If the
fitness functions are sufficiently regular, we can recast the weak formulation
in a more standard formulation, without any boundary conditions, but
supplemented by a number of conservation laws. The equations in this family can
be purely diffusive, purely hyperbolic or of convection-diffusion type, with
frequency dependent convection. The particular outcome will depend on the
assumed scalings. The diffusive equations are of the degenerate type; using a
duality approach, we also obtain a frequency dependent version of the Kimura
equation without any further assumptions. We also show that the convective
approximation is related to the replicator dynamics and provide some estimate
of how accurate is the convective approximation, with respect to the
convective-diffusion approximation. In particular, we show that the mode, but
not the expected value, of the probability distribution is modelled by the
replicator dynamics. Some numerical simulations that illustrate the results are
also presented
Black Holes in Higher Dimensions
We review black hole solutions of higher-dimensional vacuum gravity, and of
higher-dimensional supergravity theories. The discussion of vacuum gravity is
pedagogical, with detailed reviews of Myers-Perry solutions, black rings, and
solution-generating techniques. We discuss black hole solutions of maximal
supergravity theories, including black holes in anti-de Sitter space. General
results and open problems are discussed throughout.Comment: 76 pages, 14 figures; review article for Living Reviews in
Relativity. v2: some improvements and refs adde
Developing dialogue between a school subject department head and a university education researcher: convergences and divergences in experiencing educational change and complexity
This chapter explores some of the challenges and opportunities in enhancing teacherâresearcher relationships by analysing the work activities and environments of the authors, one a former secondary school teacher and subject department head and the other a university education researcher, both working in Queensland, Australia. More specifically, the chapter analyses selections from a lengthy audiorecorded interview between the authors focused on the first-named authorâs strategies for engaging with educational change in a complex school environment. The findings of this analysis highlight the mutual benefits of educators and education researchers engaging in this kind of collaboration. More broadly, such a collaboration can help to illuminate some of the wider convergences and divergences that emerge from educational change and complexity in schools and universities alike