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.
Frequently asked questions
Yes, you can cancel anytime from the Subscription tab in your account settings on the Perlego website. Your subscription will stay active until the end of your current billing period. Learn how to cancel your subscription.
At the moment all of our mobile-responsive ePub books are available to download via the app. Most of our PDFs are also available to download and we're working on making the final remaining ones downloadable now. Learn more here.
Perlego offers two plans: Essential and Complete
Essential is ideal for learners and professionals who enjoy exploring a wide range of subjects. Access the Essential Library with 800,000+ trusted titles and best-sellers across business, personal growth, and the humanities. Includes unlimited reading time and Standard Read Aloud voice.
Complete: Perfect for advanced learners and researchers needing full, unrestricted access. Unlock 1.4M+ books across hundreds of subjects, including academic and specialized titles. The Complete Plan also includes advanced features like Premium Read Aloud and Research Assistant.
Both plans are available with monthly, semester, or annual billing cycles.
We are an online textbook subscription service, where you can get access to an entire online library for less than the price of a single book per month. With over 1 million books across 1000+ topics, we’ve got you covered! Learn more here.
Look out for the read-aloud symbol on your next book to see if you can listen to it. The read-aloud tool reads text aloud for you, highlighting the text as it is being read. You can pause it, speed it up and slow it down. Learn more here.
Yes! You can use the Perlego app on both iOS or Android devices to read anytime, anywhere — even offline. Perfect for commutes or when you’re on the go. Please note we cannot support devices running on iOS 13 and Android 7 or earlier. Learn more about using the app.
Yes, you can access Black Holes: New Horizons by Sean Alan Hayward in PDF and/or ePUB format, as well as other popular books in Physical Sciences & Astronomy & Astrophysics. We have over one million books available in our catalogue for you to explore.
An Introduction to Local Black Hole Horizons in the 3+1 Approach to General Relativity∗
José Luis Jaramillo
Max-Planck-Institut für Gravitationsphysik, Albert Einstein Institut Am Muhlenberg 1, Golm D-1 44 76, Germany Jose-Luis. Jaramillo@aei. mpg. de
We present an introduction to dynamical trapping horizons as quasi-local models for black hole horizons, from the perspective of an Initial Value Problem approach to the construction of generic black hole spacetimes. We focus on the geometric and structural properties of these horizons aiming, as a main application, at the numerical evolution and analysis of black hole spacetimes in astrophysical scenarios. In this setting, we discuss their dual role as an a priori ingredient in certain formulations of Einstein equations and as an a posteriori tool for the diagnosis of dynamical black hole spacetimes. Complementary to the first-principles discussion of quasi-local horizon physics, we place an emphasis on the rigidity properties of these hypersurfaces and their role as privileged geometric probes into near-horizon strong-field spacetime dynamics.
1. Black Holes: Global vs (Quasi-)Local Approaches
1.1. Establishment's picture of the gravitational collapse
Our discussion is framed in the problem of gravitational collapse in General Relativity. The current understanding is summarized in what one could call the establishment's picture of gravitational collapse,1 a heuristic chain of results and conjectures:
(1) Singularity theorems: If gravity is able to make all light rays locally converge (namely, if trapped surfaces exist), then a spacetime singularity forms.2–5
(2) (Weak) Cosmic censorship (Conjecture): In order to preserve predictability, the formed singularity is not visible for a distant observer.6
(3) Black hole spacetimes stability (Conjecture): General Relativity gravitational dynamics drives eventually the black hole spacetime to a stationary state.
(4) Black hole uniqueness theorem: The final state is a Kerr black hole spacetime.7
* This chapter was first published in International Journal of Modern Physics D, Vol. 20, No. 11 (2011) 2169–2204
Light bending is a manifestation of spacetime curvature and black holes constitute a dramatic extreme case of this. The standard picture of gravitational collapse above suggests two (complementary) approaches to the characterization of black holes:
(a) Global approach: (weak) cosmic censorship suggests black holes as no-escape regions not extending to infinity. Its boundary defines the event horizon
(b) Quasi-local approach: Singularity theorems suggest the characterization of a black hole as a spacetime trapped region where all light rays locally converge.
