{"title":"Minimal Length Scale Scenarios for Quantum Gravity","authors":"Sabine Hossenfelder","doi":"10.12942/lrr-2013-2","DOIUrl":"https://doi.org/10.12942/lrr-2013-2","url":null,"abstract":"<p>We review the question of whether the fundamental laws of nature limit our ability to probe arbitrarily short distances. First, we examine what insights can be gained from thought experiments for probes of shortest distances, and summarize what can be learned from different approaches to a theory of quantum gravity. Then we discuss some models that have been developed to implement a minimal length scale in quantum mechanics and quantum field theory. These models have entered the literature as the generalized uncertainty principle or the modified dispersion relation, and have allowed the study of the effects of a minimal length scale in quantum mechanics, quantum electrodynamics, thermodynamics, black-hole physics and cosmology. Finally, we touch upon the question of ways to circumvent the manifestation of a minimal length scale in short-distance physics.</p>","PeriodicalId":686,"journal":{"name":"Living Reviews in Relativity","volume":"16 1","pages":""},"PeriodicalIF":40.6,"publicationDate":"2013-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.12942/lrr-2013-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5112913","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Foundations of Black Hole Accretion Disk Theory","authors":"Marek A. Abramowicz, P. Chris Fragile","doi":"10.12942/lrr-2013-1","DOIUrl":"https://doi.org/10.12942/lrr-2013-1","url":null,"abstract":"<p>This review covers the main aspects of black hole accretion disk theory. We begin with the view that one of the main goals of the theory is to better understand the nature of black holes themselves. In this light we discuss how accretion disks might reveal some of the unique signatures of strong gravity: the event horizon, the innermost stable circular orbit, and the ergosphere. We then review, from a first-principles perspective, the physical processes at play in accretion disks. This leads us to the four primary accretion disk models that we review: Polish doughnuts (thick disks), Shakura-Sunyaev (thin) disks, slim disks, and advection-dominated accretion flows (ADAFs). After presenting the models we discuss issues of stability, oscillations, and jets. Following our review of the analytic work, we take a parallel approach in reviewing numerical studies of black hole accretion disks. We finish with a few select applications that highlight particular astrophysical applications: measurements of black hole mass and spin, black hole vs. neutron star accretion disks, black hole accretion disk spectral states, and quasi-periodic oscillations (QPOs).</p>","PeriodicalId":686,"journal":{"name":"Living Reviews in Relativity","volume":"16 1","pages":""},"PeriodicalIF":40.6,"publicationDate":"2013-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.12942/lrr-2013-1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4568195","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Kerr/CFT Correspondence and its Extensions","authors":"Geoffrey Compère","doi":"10.12942/lrr-2012-11","DOIUrl":"https://doi.org/10.12942/lrr-2012-11","url":null,"abstract":"<p>We present a first-principles derivation of the main results of the Kerr/CFT correspondence and its extensions using only tools from gravity and quantum field theory, filling a few gaps in the literature when necessary. Firstly, we review properties of extremal black holes that imply, according to semi-classical quantization rules, that their near-horizon quantum states form a centrally-extended representation of the one-dimensional conformal group. This motivates the conjecture that the extremal Kerr and Reissner-Nordstr?m black holes are dual to the chiral limit of a two-dimensional CFT. We also motivate the existence of an <i>SL</i>(2, ?) family of two-dimensional CFTs, which describe in their chiral limit the extremal Kerr-Newman black hole. We present generalizations in anti-de Sitter spacetime and discuss other matter-coupling and higher-derivative corrections. Secondly, we show how a near-chiral limit of these CFTs reproduces the dynamics of near-superradiant probes around near-extremal black holes in the semi-classical limit. Thirdly, we review how the hidden conformal symmetries of asymptotically-flat black holes away from extremality, combined with their properties at extremality, allow for a microscopic accounting of the entropy of non-extremal asymptotically-flat rotating or charged black holes. We conclude with a list of open problems.</p>","PeriodicalId":686,"journal":{"name":"Living Reviews in Relativity","volume":"15 1","pages":""},"PeriodicalIF":40.6,"publicationDate":"2012-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.12942/lrr-2012-11","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5174980","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Modified Newtonian Dynamics (MOND): Observational Phenomenology and Relativistic Extensions","authors":"Benoît Famaey, Stacy S. McGaugh","doi":"10.12942/lrr-2012-10","DOIUrl":"https://doi.org/10.12942/lrr-2012-10","url":null,"abstract":"<p>A wealth of astronomical data indicate the presence of mass discrepancies in the Universe. The motions observed in a variety of classes of extragalactic systems exceed what can be explained by the mass visible in stars and gas. Either (i) there is a vast amount of unseen mass in some novel form — dark matter — or (ii) the data indicate a breakdown of our understanding of dynamics on the relevant scales, or (iii) both. Here, we first review a few outstanding challenges for the dark matter interpretation of mass discrepancies in galaxies, purely based on observations and independently of any alternative theoretical framework. We then show that many of these puzzling observations are predicted by one single relation — Milgrom’s law — involving an acceleration constant <i>a</i><sub>0</sub> (or a characteristic surface density Σ<sub>?</sub> = <i>a</i><sub>0</sub>/<i>G</i>) on the order of the square-root of the cosmological constant in natural units. This relation can at present most easily be interpreted as the effect of a single universal force law resulting from a modification of Newtonian dynamics (MOND) on galactic scales. We exhaustively review the current observational successes and problems of this alternative paradigm at all astrophysical scales, and summarize the various theoretical attempts (TeVeS, GEA, BIMOND, and others) made to effectively embed this modification of Newtonian dynamics within a relativistic theory of gravity.</p>","PeriodicalId":686,"journal":{"name":"Living Reviews in Relativity","volume":"15 1","pages":""},"PeriodicalIF":40.6,"publicationDate":"2012-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.12942/lrr-2012-10","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4320063","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Continuum and Discrete Initial-Boundary Value Problems and Einstein’s Field Equations","authors":"Olivier Sarbach, Manuel Tiglio","doi":"10.12942/lrr-2012-9","DOIUrl":"https://doi.org/10.12942/lrr-2012-9","url":null,"abstract":"<p>Many evolution problems in physics are described by partial differential equations on an infinite domain; therefore, one is interested in the solutions to such problems for a given initial dataset. A prominent example is the binary black-hole problem within Einstein’s theory of gravitation, in which one computes the gravitational radiation emitted from the inspiral of the two black holes, merger and ringdown. Powerful mathematical tools can be used to establish qualitative statements about the solutions, such as their existence, uniqueness, continuous dependence on the initial data, or their asymptotic behavior over large time scales. However, one is often interested in computing the solution itself, and unless the partial differential equation is very simple, or the initial data possesses a high degree of symmetry, this computation requires approximation by numerical discretization. When solving such discrete problems on a machine, one is faced with a finite limit to computational resources, which leads to the replacement of the infinite continuum domain with a finite computer grid. This, in turn, leads to a discrete initial-boundary value problem. The hope is to recover, with high accuracy, the exact solution in the limit where the grid spacing converges to zero with the boundary being pushed to infinity.</p><p>The goal of this article is to review some of the theory necessary to understand the continuum and discrete initial boundary-value problems arising from hyperbolic partial differential equations and to discuss its applications to numerical relativity; in particular, we present well-posed initial and initial-boundary value formulations of Einstein’s equations, and we discuss multi-domain high-order finite difference and spectral methods to solve them.</p>","PeriodicalId":686,"journal":{"name":"Living Reviews in Relativity","volume":"15 1","pages":""},"PeriodicalIF":40.6,"publicationDate":"2012-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.12942/lrr-2012-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5031032","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Binary Neutron Star Mergers","authors":"Joshua A. Faber, Frederic A. Rasio","doi":"10.12942/lrr-2012-8","DOIUrl":"https://doi.org/10.12942/lrr-2012-8","url":null,"abstract":"<p>We review the current status of studies of the coalescence of binary neutron star systems. We begin with a discussion of the formation channels of merging binaries and we discuss the most recent theoretical predictions for merger rates. Next, we turn to the quasi-equilibrium formalisms that are used to study binaries prior to the merger phase and to generate initial data for fully dynamical simulations. The quasi-equilibrium approximation has played a key role in developing our understanding of the physics of binary coalescence and, in particular, of the orbital instability processes that can drive binaries to merger at the end of their lifetimes. We then turn to the numerical techniques used in dynamical simulations, including relativistic formalisms, (magneto-)hydrodynamics, gravitational-wave extraction techniques, and nuclear microphysics treatments. This is followed by a summary of the simulations performed across the field to date, including the most recent results from both fully relativistic and microphysically detailed simulations. Finally, we discuss the likely directions for the field as we transition from the first to the second generation of gravitational-wave interferometers and while supercomputers reach the petascale frontier.</p>","PeriodicalId":686,"journal":{"name":"Living Reviews in Relativity","volume":"15 1","pages":""},"PeriodicalIF":40.6,"publicationDate":"2012-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.12942/lrr-2012-8","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4165614","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Piotr T. Chruściel, João Lopes Costa, Markus Heusler
{"title":"Stationary Black Holes: Uniqueness and Beyond","authors":"Piotr T. Chruściel, João Lopes Costa, Markus Heusler","doi":"10.12942/lrr-2012-7","DOIUrl":"https://doi.org/10.12942/lrr-2012-7","url":null,"abstract":"<p>The spectrum of known black-hole solutions to the stationary Einstein equations has been steadily increasing, sometimes in unexpected ways. In particular, it has turned out that not all black-hole-equilibrium configurations are characterized by their mass, angular momentum and global charges. Moreover, the high degree of symmetry displayed by vacuum and electro-vacuum black-hole spacetimes ceases to exist in self-gravitating non-linear field theories. This text aims to review some developments in the subject and to discuss them in light of the uniqueness theorem for the Einstein-Maxwell system.</p>","PeriodicalId":686,"journal":{"name":"Living Reviews in Relativity","volume":"15 1","pages":""},"PeriodicalIF":40.6,"publicationDate":"2012-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.12942/lrr-2012-7","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"5125539","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Dynamical Boson Stars","authors":"Steven L. Liebling, Carlos Palenzuela","doi":"10.12942/lrr-2012-6","DOIUrl":"https://doi.org/10.12942/lrr-2012-6","url":null,"abstract":"<p>The idea of stable, localized bundles of energy has strong appeal as a model for particles. In the 1950s, John Wheeler envisioned such bundles as smooth configurations of electromagnetic energy that he called <i>geons</i>, but none were found. Instead, particle-like solutions were found in the late 1960s with the addition of a scalar field, and these were given the name <i>boson stars</i>. Since then, boson stars find use in a wide variety of models as sources of dark matter, as black hole mimickers, in simple models of binary systems, and as a tool in finding black holes in higher dimensions with only a single Killing vector. We discuss important varieties of boson stars, their dynamic properties, and some of their uses, concentrating on recent efforts.</p>","PeriodicalId":686,"journal":{"name":"Living Reviews in Relativity","volume":"15 1","pages":""},"PeriodicalIF":40.6,"publicationDate":"2012-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.12942/lrr-2012-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4350898","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Quantum Measurement Theory in Gravitational-Wave Detectors","authors":"Stefan L. Danilishin, Farid Ya. Khalili","doi":"10.12942/lrr-2012-5","DOIUrl":"https://doi.org/10.12942/lrr-2012-5","url":null,"abstract":"<p>The fast progress in improving the sensitivity of the gravitational-wave detectors, we all have witnessed in the recent years, has propelled the scientific community to the point at which quantum behavior of such immense measurement devices as kilometer-long interferometers starts to matter. The time when their sensitivity will be mainly limited by the quantum noise of light is around the corner, and finding ways to reduce it will become a necessity. Therefore, the primary goal we pursued in this review was to familiarize a broad spectrum of readers with the theory of quantum measurements in the very form it finds application in the area of gravitational-wave detection. We focus on how quantum noise arises in gravitational-wave interferometers and what limitations it imposes on the achievable sensitivity. We start from the very basic concepts and gradually advance to the general linear quantum measurement theory and its application to the calculation of quantum noise in the contemporary and planned interferometric detectors of gravitational radiation of the first and second generation. Special attention is paid to the concept of the Standard Quantum Limit and the methods of its surmounting.</p>","PeriodicalId":686,"journal":{"name":"Living Reviews in Relativity","volume":"15 1","pages":""},"PeriodicalIF":40.6,"publicationDate":"2012-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.12942/lrr-2012-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4990598","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Gravitational-Wave Data Analysis. Formalism and Sample Applications: The Gaussian Case","authors":"Piotr Jaranowski, Andrzej Królak","doi":"10.12942/lrr-2012-4","DOIUrl":"https://doi.org/10.12942/lrr-2012-4","url":null,"abstract":"<p>The article reviews the statistical theory of signal detection in application to analysis of deterministic gravitational-wave signals in the noise of a detector. Statistical foundations for the theory of signal detection and parameter estimation are presented. Several tools needed for both theoretical evaluation of the optimal data analysis methods and for their practical implementation are introduced. They include optimal signal-to-noise ratio, Fisher matrix, false alarm and detection probabilities, <span>({mathcal F})</span>-statistic, template placement, and fitting factor. These tools apply to the case of signals buried in a stationary and Gaussian noise. Algorithms to efficiently implement the optimal data analysis techniques are discussed. Formulas are given for a general gravitational-wave signal that includes as special cases most of the deterministic signals of interest.</p>","PeriodicalId":686,"journal":{"name":"Living Reviews in Relativity","volume":"15 1","pages":""},"PeriodicalIF":40.6,"publicationDate":"2012-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.12942/lrr-2012-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4390116","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}