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

Isolated and dynamical horizons and their applications

Over the past three decades, black holes have played an important role in quantum gravity, mathematical physics, numerical relativity and gravitational wave phenomenology. However, conceptual settings and mathematical models used to discuss them have varied considerably from one area to another. Over the last five years a new, quasi-local framework was introduced to analyze diverse facets of black holes in a unified manner. In this framework, evolving black holes are modeled by dynamical horizons and black holes in equilibrium by isolated horizons. We review basic properties of these horizons and summarize applications to mathematical physics, numerical relativity and quantum gravity. This paradigm has led to significant generalizations of several results in black hole physics. Specifically, it has introduced a more physical setting for black hole thermodynamics and for black hole entropy calculations in quantum gravity; suggested a phenomenological model for hairy black holes; provided novel techniques to extract physics from numerical simulations; and led to new laws governing the dynamics of black holes in exact general relativity.Comment: 77 pages, 12 figures. Typos and references correcte

Harnessing learning biases is essential for applying social learning in conservation

Social learning can influence how animals respond to anthropogenic changes in the environment, determining whether animals survive novel threats and exploit novel resources or produce maladaptive behaviour and contribute to human-wildlife conflict. Predicting where social learning will occur and manipulating its use are, therefore, important in conservation, but doing so is not straightforward. Learning is an inherently biased process that has been shaped by natural selection to prioritize important information and facilitate its efficient uptake. In this regard, social learning is no different from other learning processes because it too is shaped by perceptual filters, attentional biases and learning constraints that can differ between habitats, species, individuals and contexts. The biases that constrain social learning are not understood well enough to accurately predict whether or not social learning will occur in many situations, which limits the effective use of social learning in conservation practice. Nevertheless, we argue that by tapping into the biases that guide the social transmission of information, the conservation applications of social learning could be improved. We explore the conservation areas where social learning is highly relevant and link them to biases in the cues and contexts that shape social information use. The resulting synthesis highlights many promising areas for collaboration between the fields and stresses the importance of systematic reviews of the evidence surrounding social learning practices.BBSRC David Phillips Fellowship (BB/H021817/1

Exploring new physics frontiers through numerical relativity

The demand to obtain answers to highly complex problems within strong-field gravity has been met with significant progress in the numerical solution of Einstein's equations - along with some spectacular results - in various setups. We review techniques for solving Einstein's equations in generic spacetimes, focusing on fully nonlinear evolutions but also on how to benchmark those results with perturbative approaches. The results address problems in high-energy physics, holography, mathematical physics, fundamental physics, astrophysics and cosmology

A Kinetic Approach to Hyperbolic Systems And the Role of Higher Order Entropies

Abstract. The reformulation of conservation laws in terms of kinetic equa-tions, which parallels the relation between Boltzmann and Euler equation, has been successfully used in the form of kinetic schemes. The central problem in the kinetic approach is the construction of suitable equilibrium distribu-tions which generalize the Maxwellian in the Boltzmann{Euler case. Here, we present a solution to this problem which allows the construction of equilib-rium distributions for general systems of hyperbolic conservation laws. The approach leads to the notion of higher order entropies and generalizes several approaches discussed by other authors. 1