Classical Horizons

2003 CHOICE Outstanding Academic Title This work relocates the origins of nineteenth-century social theory in classical Greece and focuses on three figures: Karl Marx, Max Weber, and Émile Durkheim, all of whom wrote dissertations on the culture and structure of ancient society. Greek philosophy, art, and politics inspired their ideas, stirred their imaginations, and defined their intellectual horizons. McCarthy rediscovers the forgotten dreams and classical horizons of these European social theorists and uncovers the close connections between sociology and philosophy, offering new insights into the methods, theories, and approaches of modern social science.

This volume offers a comprehensive guide to the extensive corpus of Jean-Luc Marion’s ideas, including a discussion of contemporary French phenomenology and critical appraisal of Marion’s ideas by leading scholars in the field. The contributors apply Marion’s thought to various fields of study, including theology, art, literature and psychology.

Black holes, once just fascinating theoretical predictions of how gravity warps space-time according to Einstein's theory, are now generally accepted as astrophysical realities, formed by post-supernova collapse, or as supermassive black holes mysteriously found at the cores of most galaxies, powering active galactic nuclei, the most powerful objects in the universe. Theoretical understanding has progressed in recent decades with a wider realization that local concepts should characterize black holes, rather than the global concepts found in textbooks. In particular, notions such as trapping horizon allow physically meaningful quantities and equations, describing how a black hole evolves. This has led to discoveries in fields as diverse as classical and numerical general relativity, differential geometry, thermodynamics, quantum field theory, and quantum gravity. There is heretofore no one volume which covers all the main aspects, so this volume collects together summaries and recent research, each chapter written by an expert or experts in a given field. This is intended for readers at a graduate level upwards, who wish to learn about the wide range of research concerning black holes. Contents:An Introduction to Local Black Hole Horizons in the 3+1 Approach to General Relativity (José Luis Jaramillo)Physical Aspects of Quasi-Local Black Hole Horizons (Alex B Nielsen)On Uniqueness Results for Static, Asymptotically Flat Initial Data Containing MOTS (Alberto Carrasco and Marc Mars)Horizons in the Near-Equilibrium Regime (Ivan Booth)Isolated Horizons in Classical and Quantum Gravity (Jonathan Engle and Tomáš Liko)Quantum Thermometers in Stationary Space-Times with Horizons (Sergio Zerbini)Relativistic Thermodynamics (Sean A Hayward)Trapped Surfaces (J M M Senovilla)Some Examples of Trapped Surfaces (I Bengtsson) Readership: Professional physicists and mathematicians. Keywords:Black HolesKey Features:Each chapter is written by an expert or experts on a given topic, up to the current state of knowledge. In this way a broad range of topics is covered in depth, which has previously been available only as individual research papers

This book overviews the extensive literature on apparent cosmological and black hole horizons. In theoretical gravity, dynamical situations such as gravitational collapse, black hole evaporation, and black holes interacting with non-trivial environments, as well as the attempts to model gravitational waves occurring in highly dynamical astrophysical processes, require that the concept of event horizon be generalized. Inequivalent notions of horizon abound in the technical literature and are discussed in this manuscript. The book begins with a quick review of basic material in the first one and a half chapters, establishing a unified notation. Chapter 2 reminds the reader of the basic tools used in the analysis of horizons and reviews the various definitions of horizons appearing in the literature. Cosmological horizons are the playground in which one should take baby steps in understanding horizon physics. Chapter 3 analyzes cosmological horizons, their proposed thermodynamics, and several coordinate systems. The remaining chapters discuss analytical solutions of the field equations of General Relativity, scalar-tensor, and f(R) gravity which exhibit time-varying apparent horizons and horizons which appear and/or disappear in pairs. An extensive bibliography enriches the volume. The intended audience is master and PhD level students and researchers in theoretical physics with knowledge of standard gravity.

One of the open challenges in fundamental physics is to combine Einstein's theory of general relativity with the principles of quantum mechancis. In this thesis, the question is raised whether metric quantum gravity could be fundamental in the spirit of Steven Weinberg's seminal asymptotic safety conjecture, and if so, what are the consequences for the physics of small, possibly Planck-size black holes? To address the first question, new techniques are provided which allow, for the first time, a self-consistent study of high-order polynomial actions including up to 34 powers in the Ricci scalar. These novel insights are then exploited to explain quantum gravity effects in black holes, including their horizon and causal structure, conformal scaling, evaporation, and the thermodynamics of quantum space-time. Results indicate upper limits on black hole temperature, and the existence of small black holes based on asymptotic safety for gravity and thermodynamical arguments.