Living Reviews in Relativity: “Entanglement Entropy of Black Holes”

Living Reviews in Relativity has published a new review article on “Entanglement Entropy of Black Holes” by Sergey N. Solodukhin on October 21, 2011.

Please find the abstract and further details below.

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PUB.NO. lrr-2011-8
Solodukhin, Sergey N.
“Entanglement Entropy of Black Holes”

ACCEPTED: 2011-08-23
PUBLISHED: 2011-10-21

FULL ARTICLE AT:
http://www.livingreviews.org/lrr-2011-8

ABSTRACT:
The entanglement entropy is a fundamental quantity which characterizes the correlations between sub-systems in a larger quantum-mechanical system. For two sub-systems separated by a surface the entanglement entropy is proportional to the area of the surface and depends on the UV cutoff which regulates the short-distance correlations. The geometrical nature of the entanglement entropy calculation is particularly intriguing when applied to black holes when the entangling surface is the black hole horizon. I review a variety of aspects of this calculation: the useful mathematical tools such as the geometry of spaces with conical singularities and the heat kernel method, the UV divergences in the entropy and their renormalization, the logarithmic terms in the entanglement entropy in four and six dimensions and their relation to the conformal anomalies. The focus in the review is on the systematic use of the conical singularity method. The relations to other known approaches such as ‘t Hooft’s brick wall model and the Euclidean path integral in the optical metric are discussed in detail. The puzzling behavior of the entanglement entropy due to fields which non-minimally couple to gravity is emphasized. The holographic description of the entanglement entropy of the black hole horizon is illustrated on the two- and four-dimensional examples. Finally, I examine the possibility to interpret the Bekenstein–Hawking entropy entirely as the entanglement entropy.

UPCOMING ARTICLES AT:
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Living Reviews in Relativity: “The Motion of Point Particles in Curved Spacetime” (update)

Living Reviews in Relativity has published a major update of the review “The Motion of Point Particles in Curved Spacetime” by Eric Poisson, Adam Pound, and Ian Vega on September 29, 2011.

Please find the abstract and further details below.

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PUB.NO. lrr-2011-7
Poisson, Eric and Pound, Adam and Vega, Ian
“The Motion of Point Particles in Curved Spacetime”

ACCEPTED: 2011-08-23
PUBLISHED: 2011-09-29

FULL ARTICLE AT:
http://www.livingreviews.org/lrr-2011-7

UPDATE NOTE:
This version of the review is a major update of the original article published in 2004. Two additional authors, Adam Pound and Ian Vega, have joined the article’s original author, and each one has contributed a major piece of the update. The literature survey presented in Sections 2 was contributed by Ian Vega, and Part V (Sections 20 to 23) was contributed by Adam Pound. Part V replaces a section of the 2004 article in which the motion of a small black hole was derived by the method of matched asymptotic expansions; this material can still be found in Ref. [142], but Pound’s work provides a much more satisfactory foundation for the gravitational self-force. The case study of Section 1.10 is new, and the ”exact” formulation of the dynamics of a point mass in Section 19.1 is a major improvement from the original article. The concluding remarks of Section 24, contributed mostly by Adam Pound, are also updated from the 2004 article. The number of references has increased from 64 to 187.

ABSTRACT:
This review is concerned with the motion of a point scalar charge, a point electric charge, and a point mass in a specified background spacetime. In each of the three cases the particle produces a field that behaves as outgoing radiation in the wave zone, and therefore removes energy from the particle. In the near zone the field acts on the particle and gives rise to a self-force that prevents the particle from moving on a geodesic of the background spacetime. The self-force contains both conservative and dissipative terms, and the latter are responsible for the radiation reaction. The work done by the self-force matches the energy radiated away by the particle.
The field’s action on the particle is difficult to calculate because of its singular nature: the field diverges at the position of the particle. But it is possible to isolate the field’s singular part and show that it exerts no force on the particle – its only effect is to contribute to the particle’s inertia. What remains after subtraction is a regular field that is fully responsible for the self-force. Because this field satisfies a homogeneous wave equation, it can be thought of as a free field that interacts with the particle; it is this interaction that gives rise to the self-force.
The mathematical tools required to derive the equations of motion of a point scalar charge, a point electric charge, and a point mass in a specified background spacetime are developed here from scratch. The review begins with a discussion of the basic theory of bitensors (Part I). It then applies the theory to the construction of convenient coordinate systems to chart a neighbourhood of the particle’s word line (Part II). It continues with a thorough discussion of Green’s functions in curved spacetime (Part III). The review presents a detailed derivation of each of the three equations of motion (Part IV). Because the notion of a point mass is problematic in general relativity, the review concludes (Part V) with an alternative derivation of the equations of motion that applies to a small body of arbitrary internal structure.

UPCOMING ARTICLES AT:
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Living Reviews in Relativity: “Coalescence of Black Hole-Neutron Star Binaries”

Living Reviews in Relativity has published a new review article on “Coalescence of Black Hole-Neutron Star Binaries” by Masaru Shibata and Keisuke Taniguchi on August 29, 2011.

Please find the abstract and further details below.

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PUB.NO. lrr-2011-6
Shibata, Masaru and Taniguchi, Keisuke
“Coalescence of Black Hole-Neutron Star Binaries”

(incl. 30 figures and 232 references)

ACCEPTED: 2011-07-07
PUBLISHED: 2011-08-29

FULL ARTICLE AT:
http://www.livingreviews.org/lrr-2011-6

ABSTRACT:
We review the current status of general relativistic studies for the coalescence of black hole-neutron star (BH-NS) binaries. First, procedures for a solution of BH-NS binaries in quasi-equilibrium circular orbits and the numerical results, such as quasi-equilibrium sequence and mass-shedding limit, of high-precision computation are summarized. Then, the current status of numerical-relativity simulations for the merger of the BH-NS binary is described. We summarize our understanding for the merger and/or tidal disruption process, the criterion for tidal disruption, the properties of the remnant formed after the tidal disruption, gravitational waveform, and gravitational-wave spectrum.

UPCOMING ARTICLES AT:
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Living Reviews in Relativity: “Gravitational Wave Detection by Interferometry” (major update)

Today, Living Reviews in Relativity has published a major update of the review “Gravitational Wave Detection by Interferometry (Ground and Space)” by Matthew Pitkin, Stuart Reid, Sheila Rowan, and Jim Hough.

Please find the abstract and further details below.

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PUB.NO. lrr-2011-5
Pitkin, Matthew, Reid, Stuart, Rowan, Sheila and Hough, James
“Gravitational Wave Detection by Interferometry (Ground and Space)”

ACCEPTED: 2011-06-17
PUBLISHED: 2011-07-11

FULL ARTICLE AT:
http://www.livingreviews.org/lrr-2011-5

UPDATE:
There have been minor updates to Sections 1, 2 and 3; major updates to Sections 4 and 5; Section 6 has been renamed and includes entirely new material on the operation of, and results from, the first generation of gravitational wave detectors and upgrades that are under way; and Section 7 also includes major updates about the status of LISA. The number of references has increased from 110 to 324.

ABSTRACT:
Significant progress has been made in recent years on the development of gravitational-wave detectors. Sources such as coalescing compact binary systems, neutron stars in low-mass X-ray binaries, stellar collapses and pulsars are all possible candidates for detection. The most promising design of gravitational-wave detector uses test masses a long distance apart and freely suspended as pendulums on Earth or in drag-free spacecraft. The main theme of this review is a discussion of the mechanical and optical principles used in the various long baseline systems in operation around the world – LIGO (USA), Virgo (Italy/France), TAMA300 and LCGT (Japan), and GEO600 (Germany/U.K.) – and in LISA, a proposed space-borne interferometer. A review of recent science runs from the current generation of ground-based detectors will be discussed, in addition to highlighting the astrophysical results gained thus far. Looking to the future, the major upgrades to LIGO (Advanced LIGO), Virgo (Advanced Virgo), LCGT and GEO600 (GEO-HF) will be completed over the coming years, which will create a network of detectors with the significantly improved sensitivity required to detect gravitational waves. Beyond this, the concept and design of possible future “third generation” gravitational-wave detectors, such as the Einstein Telescope (ET), will be discussed.

UPCOMING ARTICLES AT:
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Living Reviews in Relativity: “Analogue Gravity” and “The Einstein-Vlasov System/Kinetic Theory” (updates)

This month, Living Reviews in Relativity has published two major updates of the reviews “The Einstein-Vlasov System/Kinetic Theory” by Håkan Andréasson and “Analogue Gravity” by Carlos Barceló, Stefano Liberati and Matt Visser. Both articles substantially revise previous versions from 2005.

Please find the abstract and further details below.

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PUB.NO. lrr-2011-4
Andréasson, Håkan
“The Einstein-Vlasov System/Kinetic Theory”

ACCEPTED: 2011-05-06
PUBLISHED: 2011-05-27

FULL ARTICLE AT:
http://www.livingreviews.org/lrr-2011-4

UPDATE:
This is a revised and updated version of the article from 2005. A number of new sections on the Einstein-Vlasov system have been added, e.g., on the formation of black holes and trapped surfaces, on self-similar solutions, on the structure of static solutions, on Buchdahl type inequalities, on the stability of cosmological solutions, and on axisymmetric solutions. Some of the previous sections have been significantly extended. The number of references has increased from 121 to 197.

ABSTRACT:
The main purpose of this article is to provide a guide to theorems on global properties of solutions to the Einstein–Vlasov system. This system couples Einstein’s equations to a kinetic matter model. Kinetic theory has been an important field of research during several decades in which the main focus has been on non-relativistic and special relativistic physics, i.e., to model the dynamics of neutral gases, plasmas, and Newtonian self-gravitating systems. In 1990, Rendall and Rein initiated a mathematical study of the Einstein–Vlasov system. Since then many theorems on global properties of solutions to this system have been established. This paper gives introductions to kinetic theory in non-curved spacetimes and then the Einstein–Vlasov system is introduced. We believe that a good understanding of kinetic theory in non-curved spacetimes is fundamental to a good comprehension of kinetic theory in general relativity.

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PUB.NO. lrr-2011-3
Barceló Serón, Carlos and Liberati, Stefano and Visser, Matt
“Analogue Gravity”

ACCEPTED: 2011-02-28
PUBLISHED: 2011-05-11

FULL ARTICLE AT:
http://www.livingreviews.org/lrr-2011-3

UPDATE:
Completely revised and updated previous version. Significantly extended Sections 2.4, 3, 4.1, 4.2, 5, and 7. Introduced new Section 6. Eight new figures have been added. The number of references increased from 434 to 702.

ABSTRACT:
Analogue gravity is a research programme which investigates analogues of general relativistic gravitational fields within other physical systems, typically but not exclusively condensed matter systems, with the aim of gaining new insights into their corresponding problems. Analogue models of (and for) gravity have a long and distinguished history dating back to the earliest years of general relativity. In this review article we will discuss the history, aims, results, and future prospects for the various analogue models. We start the discussion by presenting a particularly simple example of an analogue model, before exploring the rich history and complex tapestry of models discussed in the literature. The last decade in particular has seen a remarkable and sustained development of analogue gravity ideas, leading to some hundreds of published articles, a workshop, two books, and this review article. Future prospects for the analogue gravity programme also look promising, both on the experimental front (where technology is rapidly advancing) and on the theoretical front (where variants of analogue models can be used as a springboard for radical attacks on the problem of quantum gravity).

UPCOMING ARTICLES AT:
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Living Reviews in Relativity – No. 100: “Varying Constants, Gravitation and Cosmology”

Today, Living Reviews in Relativity has published a new review article on “Varying Constants, Gravitation and Cosmology” by Jean-Philippe Uzan. Please find the abstract and further details below.

THIS IS PUBLICATION NO. 100!

Thus, our journal offers 100 review articles on 72 different topics in in various areas of relativity. All full texts are free of charge, following the principles of the Open Access to Scientific Knowledge movement. Our reference database now contains about 20,000 references which are linked to the reviews and can be exported in various formats.

The success of Living Reviews in Relativity has been acknowledged by its high Impact Factor (10.600), and just recently by SPIRES including 10 reviews in the Top Cited Articles during 2010 in gr-qc. Overall, nine articles made it to the list of the 100 most highly cited papers of all time.

We’d like to thank all our readers and authors for their interest and support!

The Living Reviews team.

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PUB.NO. lrr-2011-2
Uzan, Jean-Philippe
“Varying Constants, Gravitation and Cosmology”

ACCEPTED: 2011-03-23
PUBLISHED: 2011-03-29

FULL ARTICLE AT:
http://www.livingreviews.org/lrr-2011-2

(incl. 6 Figures and 554 references)

ABSTRACT:
Fundamental constants are a cornerstone of our physical laws. Any constant varying in space and/or time would reflect the existence of an almost massless field that couples to matter. This will induce a violation of the universality of free fall. Thus, it is of utmost importance for our understanding of gravity and of the domain of validity of general relativity to test for their constancy. We detail the relations between the constants, the tests of the local position invariance and of the universality of free fall. We then review the main experimental and observational constraints that have been obtained from atomic clocks, the Oklo phenomenon, solar system observations, meteorite dating, quasar absorption spectra, stellar physics, pulsar timing, the cosmic microwave background and big bang nucleosynthesis. At each step we describe the basics of each system, its dependence with respect to the constants, the known systematic effects and the most recent constraints that have been obtained. We then describe the main theoretical frameworks in which the low-energy constants may actually be varying and we focus on the unification mechanisms and the relations between the variation of different constants. To finish, we discuss the more speculative possibility of understanding their numerical values and the apparent fine-tuning that they confront us with.

UPCOMING ARTICLES AT:
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Living Reviews in Relativity
http://relativity.livingreviews.org/
ISSN: 1433-8351

Published by
Max Planck Institute for Gravitational Physics
(Albert Einstein Institute)

Living Reviews in Relativity: “Gravitational Waves from Gravitational Collapse” (update)

Living Reviews in Relativity has published a major update of the review “Gravitational Waves from Gravitational Collapse” by Chris L. Fryer and Kimberly C.B. New on January 20, 2011.

Please find the abstract and further details below.

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PUB.NO. lrr-2011-1
Fryer, Chris L. and New, Kimberly C. B.
“Gravitational Waves from Gravitational Collapse”

ACCEPTED: 2011-01-14
PUBLISHED: 2011-01-20

FULL ARTICLE AT:
http://www.livingreviews.org/lrr-2011-1

UPDATE:
We have significantly altered and restructured the text of the previous version, describing the latest results from a new point of view. New figures have been added. The number of references has increased from 271 to 350.

ABSTRACT:
Gravitational wave emission from stellar collapse has been studied for nearly four decades. Current state-of-the-art numerical investigations of collapse include those that use progenitors with more realistic angular momentum profiles, properly treat microphysics issues, account for general relativity, and examine non-axisymmetric effects in three dimensions. Such simulations predict that gravitational waves from various phenomena associated with gravitational collapse could be detectable with ground-based and space-based interferometric observatories. This review covers the entire range of stellar collapse sources of gravitational waves: from the accretion induced collapse of a white dwarf through the collapse down to neutron stars or black holes of massive stars to the collapse of supermassive stars.

UPCOMING ARTICLES AT:
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Living Reviews in Relativity: “Quantization of Midisuperspace Models”

Living Reviews in Relativity has published a new review article on “Quantization of Midisuperspace Models” by J. Fernando Barbero González and Eduardo J.S. Villaseñor on October 14, 2010.

Please find the abstract and further details below.

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PUB.NO. lrr-2010-6
Barbero G., J. Fernando and Villaseñor, Eduardo J.S.
“Quantization of Midisuperspace Models”

ACCEPTED: 2010-09-28
PUBLISHED: 2010-10-14

FULL ARTICLE AT:
http://www.livingreviews.org/lrr-2010-6

ABSTRACT:
We give a comprehensive review of the quantization of midisuperspace models. Though the main focus of the paper is on quantum aspects, we also provide an introduction to several classical points related to the definition of these models. We cover some important issues, in particular, the use of the principle of symmetric criticality as a very useful tool to obtain the required Hamiltonian formulations. Two main types of reductions are discussed: those involving metrics with two Killing vector fields and spherically-symmetric models. We also review the more general models obtained by coupling matter fields to these systems. Throughout the paper we give separate discussions for standard quantizations using geometrodynamical variables and those relying on loop-quantum-gravity–inspired methods.

UPCOMING ARTICLES AT:
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Living Reviews in Relativity: Updated Articles

Living Reviews in Relativity has published a major update of the review “Brane-World Gravity” by Roy Maartens and Kazuya Koyama on 14 September 2010.

The original article by Roy Maartens from 2004 ranks number 13 on SPIRES “Top Cited Articles of All Time (2009 edition) in gr-qc”.

Please, note also the revision of the review “Analytic Black Hole Perturbation Approach to Gravitational Radiation” by Misao Sasaki and Hideyuki Tagoshi.

Find the further details on these revisions below.

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PUB.NO. lrr-2010-5
Maartens, Roy and Koyama, Kazuya
“Brane-World Gravity”

ACCEPTED: 2010-09-06
PUBLISHED: 2010-09-14

FULL ARTICLE AT:
http://www.livingreviews.org/lrr-2010-5

UPDATE:
Inserted subsections on numerical solutions in Sections 6 and 7 and five figures. Added new Subsection 2.2 on the Randall–Sundrum model in string theory. Added new Section 9 on Dvali–Gabadadze–Porrati models and nine figures. Added new Section 10 on 6-dimensional models and one figure. Added about 100 new references.

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PUB.NO. lrr-2003-6
Sasaki, Misao and Tagoshi, Hideyuki
“Analytic Black Hole Perturbation Approach to Gravitational Radiation”

ACCEPTED: 2010-08-24
PUBLISHED: 2010-09-14

FULL ARTICLE AT:
http://www.livingreviews.org/lrr-2003-6

UPDATE:
The main changes are new Sections 4.6, 5.3, 5.8, and 5.9, which show the progress since 2003. Added 46 new references.

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UPCOMING ARTICLES AT:
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Living Reviews in Relativity: “The Pioneer Anomaly”

Living Reviews in Relativity has published a new review article on “The Pioneer Anomaly” by Slava G. Turyshev and Viktor T. Toth on September 1, 2010.

Please find the abstract and further details below.

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PUB.NO. lrr-2010-4
Turyshev, Slava and Toth, Viktor T.
“The Pioneer Anomaly”

ACCEPTED: 2010-07-16
PUBLISHED: 2010-09-01

FULL ARTICLE AT:
http://www.livingreviews.org/lrr-2010-4

ABSTRACT:
Radio-metric Doppler tracking data received from the Pioneer 10 and 11 spacecraft from heliocentric distances of 20-70 AU has consistently indicated the presence of a small, anomalous, blue-shifted frequency drift uniformly changing with a rate of $sim 6times 10^{-9}$ Hz/s. Ultimately, the drift was interpreted as a constant sunward deceleration of each particular spacecraft at the level of $a_P = (8.74 pm 1.33)times 10^{-10}$ m/s$^2$. This apparent violation of the Newton’s gravitational inverse square law has become known as the Pioneer anomaly; the nature of this anomaly remains unexplained. In this review, we summarize the current knowledge of the physical properties of the anomaly and the conditions that led to its detection and characterization. We review various mechanisms proposed to explain the anomaly and discuss the current state of efforts to determine its nature. A comprehensive new investigation of the anomalous behavior of the two Pioneers has begun recently. The new efforts rely on the much-extended set of radio-metric Doppler data for both spacecraft in conjunction with the newly available complete record of their telemetry files and a large archive of original project documentation. As the new study is yet to report its findings, this review provides the necessary background for the new results to appear in the near future. In particular, we provide a significant amount of information on the design, operations and behavior of the two Pioneers during their entire missions, including descriptions of various data formats and techniques used for their navigation and radio-science data analysis. As most of this information was recovered relatively recently, it was not used in the previous studies of the Pioneer anomaly, but it is critical for the new investigation.

UPCOMING ARTICLES AT:
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Living Reviews in Relativity: “Cosmic Censorship for Gowdy Spacetimes”

Living Reviews in Relativity
http://relativity.livingreviews.org/
ISSN: 1433-8351

Living Reviews in Relativity has published a new review article on “Cosmic Censorship for Gowdy Spacetimes” by Hans Ringström on April 13, 2010.

Please find the abstract and further details below.

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PUB.NO. lrr-2010-2
Ringström, Hans
“Cosmic Censorship for Gowdy Spacetimes”

FULL ARTICLE AT:
http://www.livingreviews.org/lrr-2010-2

ACCEPTED: 2010-03-29
PUBLISHED: 2010-04-13

(incl. 91 references and 5 figures)

ABSTRACT:
Due to the complexity of Einstein’s equations, it is often natural to study a question of interest in the framework of a restricted class of solutions. One way to impose a restriction is to consider solutions satisfying a given symmetry condition. There are many possible choices, but the present article is concerned with one particular choice, which we shall refer to as Gowdy symmetry. We begin the article by explaining the origin and meaning of this symmetry type, which has been used as a simplifying assumption in various contexts, some of which we shall mention. Nevertheless, the subject of interest here is strong cosmic censorship. Consequently, after having described what the Gowdy class of spacetimes is, we describe, as seen from the perspective of a mathematician, what is meant by strong cosmic censorship. The existing results on cosmic censorship are based on a detailed analysis of the asymptotic behaviour of solutions. This analysis is in part motivated by conjectures, such as the BKL conjecture, which we shall therefore briefly describe. However, the emphasis of the article is on the mathematical analysis of the asymptotics, due to its central importance in the proof as well as to the hope that it might be of relevance more generally. The article ends with a description of the results that have been obtained concerning strong cosmic censorship in the class of Gowdy spacetimes.

UPCOMING ARTICLES AT:
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Living Reviews in Relativity: “Interferometer Techniques for Gravitational-Wave Detection”

Living Reviews in Relativity
http://relativity.livingreviews.org/
ISSN: 1433-8351

Today, Living Reviews in Relativity has published a new review article on “Interferometer Techniques for Gravitational-Wave Detection” by Andreas Freise and Kenneth A. Strain.

Find the abstract and further details below.

Please, note also the latest revision of the review on “Critical Phenomena in Gravitational Collapse” by Carsten Gundlach and José M. Martín-García (http://www.livingreviews.org/lrr-2007-5).

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PUB.NO. lrr-2010-1
Strain, Kenneth A. and Freise, Andreas
“Interferometer Techniques for Gravitational-Wave Detection”

ACCEPTED: 2010-02-15
PUBLISHED: 2010-02-25

FULL ARTICLE AT:
http://www.livingreviews.org/lrr-2010-1

ABSTRACT:
Several km-scale gravitational wave detectors have been constructed world wide. These instruments combine a number of advanced technologies to push the limits of precision length measurement. The core devices are laser interferometers of a new kind; developed from the classical Michelson topology these interferometers integrate additional optical elements which significantly change the properties of the optical system. Much of the design and analysis of these laser interferometers can be performed using well-known classical optical techniques, however, the complex optical layouts provide a new challenge. In this review we give a textbook style introduction to the optical science required for the understanding of modern gravitational wave detectors, as well as other high-precision laser interferometers. In addition, we provide a number of examples for a freely available interferometer simulation software and encourage the reader to use these examples to gain hands-on experience with the discussed optical methods.

UPCOMING ARTICLES AT:
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Living Reviews in Relativity: “Null Geodesic Congruences…”

Living Reviews in Relativity
http://relativity.livingreviews.org/
ISSN: 1433-8351

11 September 2009

Today, Living Reviews in Relativity has published a new review article on “Null Geodesic Congruences, Asymptotically Flat Spacetimes and Their Physical Interpretation” by Timothy M. Adamo and Carlos Kozameh and Ezra T. Newman.

Please find the abstract and further details below.

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PUB.NO. lrr-2009-6
Adamo, Timothy M. and Kozameh, Carlos and Newman, Ezra T.
“Null Geodesic Congruences, Asymptotically-Flat Spacetimes and Their Physical Interpretation”

ACCEPTED: 2009-08-05
PUBLISHED: 2009-09-11

ABSTRACT:
A priori, there is nothing very special about shear-free or asymptotically shear-free null geodesic congruences. Surprisingly, however, they turn out to possess a large number of fascinating geometric properties and to be closely related, in the context of general relativity, to a variety of physically significant effects. It is the purpose of this paper to try to fully develop these issues.

This work starts with a detailed exposition of the theory of shear-free and asymptotically shear-free null geodesic congruences, i.e., congruences with shear that vanishes at future conformal null infinity. A major portion of the exposition lies in the analysis of the space of regular shear-free and asymptotically shear-free null geodesic congruences. This analysis leads to the space of complex analytic curves in complex Minkowski space. They in turn play a dominant role in the applications.

The applications center around the problem of extracting interior physical properties of an asymptotically-flat spacetime directly from the asymptotic gravitational (and Maxwell) field itself, in analogy with the determination of total charge by an integral over the Maxwell field at infinity or the identification of the interior mass (and its loss) by (Bondi’s) integrals of the Weyl tensor, also at infinity.

More specifically, we will see that the asymptotically shear-free congruences lead us to an asymptotic definition of the center-of-mass and its equations of motion. This includes a kinematic meaning, in terms of the center-of-mass motion, for the Bondi three-momentum. In addition, we obtain insights into intrinsic spin and, in general, angular momentum, including an angular-momentum–conservation law with well-defined flux terms. When a Maxwell field is present, the asymptotically shear-free congruences allow us to determine/define at infinity a center-of-charge world line and intrinsic magnetic dipole moment.

The work ends with appendices relating the shear-free congruences asymptotic twistor space and an induced CR structure on future null infinity.

FULL ARTICLE AT:
http://www.livingreviews.org/lrr-2009-6

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