Eric Gourgoulhon

Bio: Eric Gourgoulhon is an academic researcher from University of Paris. The author has contributed to research in topics: Neutron star & General relativity. The author has an hindex of 43, co-authored 187 publications receiving 5983 citations. Previous affiliations of Eric Gourgoulhon include Paris Observatory & Paris Diderot University.

3+1 Formalism and Bases of Numerical Relativity

Abstract: These lecture notes provide some introduction to the 3+1 formalism of general relativity, which is the foundation of most modern numerical relativity. The text is rather self-contained, with detailed calculations and numerous examples. Contents: 1. Introduction, 2. Geometry of hypersurfaces, 3. Geometry of foliations, 4. 3+1 decomposition of Einstein equation, 5. 3+1 equations for matter and electromagnetic field, 6. Conformal decomposition, 7. Asymptotic flatness and global quantities, 8. The initial data problem, 9. Choice of foliation and spatial coordinates, 10. Evolution schemes.

Prospects for Fundamental Physics with LISA

Abstract: In this paper, which is of programmatic rather than quantitative nature, we aim to further delineate and sharpen the future potential of the LISA mission in the area of fundamental physics. Given the very broad range of topics that might be relevant to LISA, we present here a sample of what we view as particularly promising directions, based in part on the current research interests of the LISA scientific community in the area of fundamental physics. We organize these directions through a "science-first" approach that allows us to classify how LISA data can inform theoretical physics in a variety of areas. For each of these theoretical physics classes, we identify the sources that are currently expected to provide the principal contribution to our knowledge, and the areas that need further development. The classification presented here should not be thought of as cast in stone, but rather as a fluid framework that is amenable to change with the flow of new insights in theoretical physics.

Numerical Relativity: Solving Einstein's Equations on the Computer

Abstract: Numerical relativity is one of the major fields of contemporary general relativity and is developing continually. Yet three years ago, no textbook was available on this subject. The first textbook devoted to numerical relativity, by Alcubierre, appeared in 2008 [1] (cf the CQG review [2]). Now comes the second book, by Baumgarte and Shapiro, two well known players in the field. Inevitably, the two books have some common aspects (otherwise they would not deal with the same topic!). For instance the titles of the first four chapters of Baumgarte and Shapiro are very similar to those of Alcubierre. This arises from some logic inherent to the subject: chapter 1 recaps basic GR, chapter 2 introduces the 3+1 formalism, chapter 3 focuses on the initial data and chapter 4 on the choice of coordinates for the evolution. But there are also many differences between the two books, which actually make them complementary. At first glance the differences are the size (720 pages for Baumgarte and Shapiro vs 464 pages for Alcubierre) and the colour figures in Baumgarte and Shapiro. Regarding the content, Baumgarte and Shapiro address many topics which are not present in Alcubierre's book, such as magnetohydrodynamics, radiative transfer, collisionless matter, spectral methods, rotating stars and post-Newtonian approximation. The main difference regards binary systems: virtually absent from Alcubierre's book (except for binary black hole initial data), they occupy not less than five chapters in Baumgarte and Shapiro's book. In contrast, gravitational wave extraction, various hyperbolic formulations of Einstein's equations and the high-resolution shock-capturing schemes are treated in more depth by Alcubierre. In the first four chapters mentioned above, some distinctive features of Baumgarte and Shapiro's book are the beautiful treatment of Oppenheimer–Snyder collapse in chapter 1, the analogy with Maxwell's equations when discussing the constraints and the evolution equations in chapter 2 and the nice illustration of the 3+1 formalism by different slicings of Schwarzschild spacetime. Chapter 3, devoted to initial data, presents the York–Lichnerowicz conformal method with many details and examples, along with its descendants (extended conformal thin-sandwich). A very instructive illustration is provided by a boosted black hole. This chapter also introduces the recent waveless approximation and presents a rather detailed discussion of mass, momentum and angular momentum in the initial data. Chapter 4 contains a very pedagogical discussion of the choice of coordinates, via the lapse and shift functions, again with many examples. In particular, it provides the derivation of all maximal slicings of Schwarzschild spacetime, which is hardly found in any textbook. Chapter 5, devoted to matter sources, goes well beyond the ideal fluid generally discussed in the context of 3+1 numerical relativity: it also covers dissipative fluids, radiation hydrodynamics, collisionless matter and scalar fields. Chapter 6 provides a self-consistent introduction to the two main numerical methods used in numerical relativity: finite differences and spectral methods. It is followed by a very nice chapter about the various horizons involved in black hole spacetimes: event and apparent horizons, as well as dynamical and isolated horizons. One may, however, regret that there is no mention of Hayward's trapping horizons, which embody both dynamical and isolated horizons. Chapter 8 discusses in depth spherical spacetimes, including dynamical slicings of Schwarzschild, gravitational collapse of collisionless matter (26 pages!), collapse of fluid stars and scalar fields and critical phenomena. The main outcome of numerical relativity, gravitational waves, are introduced in a very pedagogical way in chapter 9, with the basic theory and a review of the astrophysical sources and detectors. Chapter 10, entirely devoted to the axisymmetric collapse of collisionless clusters, reflects clearly the research work of one of the authors, but it is also an opportunity to discuss the Cosmic Censorship conjecture and the Hoop conjecture. Chapter 11 presents the basics of hyperbolic systems and focuses on the famous BSSN formalism employed in most numerical codes. The electromagnetism analogy introduced in chapter 2 is developed, providing some very useful insight. The remainder of the book is devoted to the collapse of rotating stars (chapter 14) and to the coalescence of binary systems of compact objects, either neutron stars or black holes (chapters 12, 13, 15, 16 and 17). This is a unique introduction and review of results about the expected main sources of gravitational radiation. It includes a detailed presentation of the major triumph of numerical relativity: the successful computation of binary black hole merger. I think that Baumgarte and Shapiro have accomplished a genuine tour de force by writing such a comprehensive and self-contained textbook on a highly evolving subject. The primary value of the book is to be extremely pedagogical. The style is definitively at the textbook level and not that of a review article. One may point out the use of boxes to recap important results and the very instructive aspect of many figures, some of them in colour. There are also numerous exercises in the main text, to encourage the reader to find some useful results by himself. The pedagogical trend is manifest up to the book cover, with the subtitle explaining what the title means! Another great value of the book is indisputably its encyclopedic aspect, making it a very good starting point for research on many topics of modern relativity. I have no doubt that Baumgarte and Shapiro's monograph will quicken considerably the learning phase of any master or PhD student beginning numerical relativity. It will also prove to be very valuable for all researchers of the field and should become a major reference. Beyond numerical relativity, the richness and variety of examples are such that the reading of the book will be highly profitable to any person interested in black hole physics or relativistic astrophysics. This is not the least among all the merits of this superb book. References [1] Alcubierre M 2008 Introduction to 3+1 Numerical Relativity (Oxford: Oxford University Press) [2] Gundlach C 2008 Review of Introduction to 3+1 Numerical Relativity Class. Quantum Grav. 278 1270

I and i

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

The Observation of Gravitational Waves from a Binary Black Hole Merger

Abstract: On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal. The signal sweeps upwards in frequency from 35 to 250 Hz with a peak gravitational-wave strain of 1.0×10(-21). It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203,000 years, equivalent to a significance greater than 5.1σ. The source lies at a luminosity distance of 410(-180)(+160) Mpc corresponding to a redshift z=0.09(-0.04)(+0.03). In the source frame, the initial black hole masses are 36(-4)(+5)M⊙ and 29(-4)(+4)M⊙, and the final black hole mass is 62(-4)(+4)M⊙, with 3.0(-0.5)(+0.5)M⊙c(2) radiated in gravitational waves. All uncertainties define 90% credible intervals. These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first direct detection of gravitational waves and the first observation of a binary black hole merger.

The Confrontation Between General Relativity and Experiment

Abstract: The status of experimental tests of general relativity and of theoretical frameworks for analyzing them is reviewed and updated. Einstein’s equivalence principle (EEP) is well supported by experiments such as the Eotvos experiment, tests of local Lorentz invariance and clock experiments. Ongoing tests of EEP and of the inverse square law are searching for new interactions arising from unification or quantum gravity. Tests of general relativity at the post-Newtonian level have reached high precision, including the light deflection, the Shapiro time delay, the perihelion advance of Mercury, the Nordtvedt effect in lunar motion, and frame-dragging. Gravitational wave damping has been detected in an amount that agrees with general relativity to better than half a percent using the Hulse-Taylor binary pulsar, and a growing family of other binary pulsar systems is yielding new tests, especially of strong-field effects. Current and future tests of relativity will center on strong gravity and gravitational waves.

Gravitational Waves and Gamma-Rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A

Abstract: On 2017 August 17, the gravitational-wave event GW170817 was observed by the Advanced LIGO and Virgo detectors, and the gamma-ray burst (GRB) GRB 170817A was observed independently by the Fermi Gamma-ray Burst Monitor, and the Anti-Coincidence Shield for the Spectrometer for the International Gamma-Ray Astrophysics Laboratory. The probability of the near-simultaneous temporal and spatial observation of GRB 170817A and GW170817 occurring by chance is $5.0\times {10}^{-8}$. We therefore confirm binary neutron star mergers as a progenitor of short GRBs. The association of GW170817 and GRB 170817A provides new insight into fundamental physics and the origin of short GRBs. We use the observed time delay of $(+1.74\pm 0.05)\,{\rm{s}}$ between GRB 170817A and GW170817 to: (i) constrain the difference between the speed of gravity and the speed of light to be between $-3\times {10}^{-15}$ and $+7\times {10}^{-16}$ times the speed of light, (ii) place new bounds on the violation of Lorentz invariance, (iii) present a new test of the equivalence principle by constraining the Shapiro delay between gravitational and electromagnetic radiation. We also use the time delay to constrain the size and bulk Lorentz factor of the region emitting the gamma-rays. GRB 170817A is the closest short GRB with a known distance, but is between 2 and 6 orders of magnitude less energetic than other bursts with measured redshift. A new generation of gamma-ray detectors, and subthreshold searches in existing detectors, will be essential to detect similar short bursts at greater distances. Finally, we predict a joint detection rate for the Fermi Gamma-ray Burst Monitor and the Advanced LIGO and Virgo detectors of 0.1–1.4 per year during the 2018–2019 observing run and 0.3–1.7 per year at design sensitivity.

First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole

Abstract: When surrounded by a transparent emission region, black holes are expected to reveal a dark shadow caused by gravitational light bending and photon capture at the event horizon. To image and study this phenomenon, we have assembled the Event Horizon Telescope, a global very long baseline interferometry array observing at a wavelength of 1.3 mm. This allows us to reconstruct event-horizon-scale images of the supermassive black hole candidate in the center of the giant elliptical galaxy M87. We have resolved the central compact radio source as an asymmetric bright emission ring with a diameter of 42 +/- 3 mu as, which is circular and encompasses a central depression in brightness with a flux ratio greater than or similar to 10: 1. The emission ring is recovered using different calibration and imaging schemes, with its diameter and width remaining stable over four different observations carried out in different days. Overall, the observed image is consistent with expectations for the shadow of a Kerr black hole as predicted by general relativity. The asymmetry in brightness in the ring can be explained in terms of relativistic beaming of the emission from a plasma rotating close to the speed of light around a black hole. We compare our images to an extensive library of ray-traced general-relativistic magnetohydrodynamic simulations of black holes and derive a central mass of M = (6.5 +/- 0.7) x 10(9) M-circle dot. Our radio-wave observations thus provide powerful evidence for the presence of supermassive black holes in centers of galaxies and as the central engines of active galactic nuclei. They also present a new tool to explore gravity in its most extreme limit and on a mass scale that was so far not accessible.