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

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

Loop Quantum Gravity

The problem of finding the quantum theory of the gravitational field, and thus understanding what is quantum spacetime, is still open. One of the most active of the current approaches is loop quantum gravity. Loop quantum gravity is a mathematically well-defined, non-perturbative and background independent quantization of general relativity, with its conventional matter couplings. The research in loop quantum gravity forms today a vast area, ranging from mathematical foundations to physical applications. Among the most significative results obtained are: (i) The computation of the physical spectra of geometrical quantities such as area and volume; which yields quantitative predictions on Planck-scale physics. (ii) A derivation of the Bekenstein-Hawking black hole entropy formula. (iii) An intriguing physical picture of the microstructure of quantum physical space, characterized by a polymer-like Planck scale discreteness. This discreteness emerges naturally from the quantum theory and provides a mathematically well-defined realization of Wheeler's intuition of a spacetime ``foam''. Long standing open problems within the approach (lack of a scalar product, overcompleteness of the loop basis, implementation of reality conditions) have been fully solved. The weak part of the approach is the treatment of the dynamics: at present there exist several proposals, which are intensely debated. Here, I provide a general overview of ideas, techniques, results and open problems of this candidate theory of quantum gravity, and a guide to the relevant literature.Comment: Review paper written for the electronic journal `Living Reviews'. 34 page

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

Are hedgerows effective corridors between fragments of woodland habitat? An evidence-based approach

Anthropogenic modification of the countryside has resulted in much of the landscape consisting of fragments of once continuous habitat. Increasing habitat connectivity at the landscape-scale has a vital role to play in the conservation of species restricted to such remnant patches, especially as species may attempt to track zones of habitat that satisfy their niche requirements as the climate changes. Conservation policies and management strategies frequently advocate corridor creation as one approach to restore connectivity and to facilitate species movements through the landscape. Here we examine the utility of hedgerows as corridors between woodland habitat patches using rigorous systematic review methodology. Systematic searching yielded 26 studies which satisfied the review inclusion criteria. The empirical evidence currently available is insufficient to evaluate the effectiveness of hedgerow corridors as a conservation tool to promote the population viability of woodland fauna. However, the studies did provide anecdotal evidence of positive local population effects and indicated that some species use hedgerows as movement conduits. More replicated and controlled field investigations or long term monitoring are required in order to allow practitioners and policy makers to make better informed decisions about hedgerow corridor creation and preservation. The benefits of such corridors in regard to increasing habitat connectivity remain equivocal, and the role of corridors in mitigating the effects of climate change at the landscape-scale is even less well understood

Challenges in Turbulent Mixing with Combustion

Turbulent combustion combines the complexities of turbulence and mixing, challenges not met in the twentieth century, with the complexity and subtlety of chemical kinetics. This discussion focuses on progress and some turbulent-mixing issues in chemically reacting flows stemming from experimental, modeling, and direct-numerical simulation (DNS) studies. The mixing transition will be discussed. DNS studies of the Rayleigh-Taylor instability in miscible fluids reveal an early-time diffusive growth and a strong sensitivity to initial conditions. Recent experiments address the assumption of isotropy in turbulence and mixing. Experiments in high-speed shear layers elucidate some effects of compressibility on the mixed-fluid field. Issues involving molecular-transport coefficients will also be discussed

Threats from climate change to terrestrial vertebrate hotspots in europe.

We identified hotspots of terrestrial vertebrate species diversity in Europe and adjacent islands. Moreover, we assessed the extent to which by the end of the 21(st) century such hotspots will be exposed to average monthly temperature and precipitation patterns which can be regarded as extreme if compared to the climate experienced during 1950-2000. In particular, we considered the entire European sub-continent plus Turkey and a total of 1149 species of terrestrial vertebrates. For each species, we developed species-specific expert-based distribution models (validated against field data) which we used to calculate species richness maps for mammals, breeding birds, amphibians, and reptiles. Considering four global circulation model outputs and three emission scenarios, we generated an index of risk of exposure to extreme climates, and we used a bivariate local Moran's I to identify the areas with a significant association between hotspots of diversity and high risk of exposure to extreme climates. Our results outline that the Mediterranean basin represents both an important hotspot for biodiversity and especially for threatened species for all taxa. In particular, the Iberian and Italian peninsulas host particularly high species richness as measured over all groups, while the eastern Mediterranean basin is particularly rich in amphibians and reptiles; the islands (both Macaronesian and Mediterranean) host the highest richness of threatened species for all taxa occurs. Our results suggest that the main hotspots of biodiversity for terrestrial vertebrates may be extensively influenced by the climate change projected to occur over the coming decades, especially in the Mediterranean bioregion, posing serious concerns for biodiversity conservation