DOCSLIB.ORG

Gravitational-Wave (Astro)Physics: from Theory to Data and Back

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Gravitational-Wave (Astro)Physics: from Theory to Data and Back Gravitational-Wave (Astro)Physics: from Theory to Data and Back Alessandra Buonanno Max Planck Institute for Gravitational Physics (Albert Einstein Institute) Department of Physics, University of Maryland Spitzer Lectures, Princeton University April 26, 2018 Spitzer Lectures •Lecture I: Basics of gravitational-wave theory and modeling •Lecture II: Advanced methods to solve the two-body problem in General Relativity •Lecture III: Inferring cosmology and astrophysics with gravitational- wave observations •Lecture IV: Probing dynamical gravity and extreme matter with gravitational-wave observations (NR simulation: Ossokine, AB & SXS @AEI) (visualization credit: Benger @ Airborne Hydro Mapping Software & Haas @AEI) References: • M. Maggiore’s books: “Gravitational Waves Volume 1: Theory and Experiments” (2007) & “Gravitational Waves Volume II: Astrophysics and Cosmology” (2018). • E. Poisson & C. Will’s book: “Gravity” (2015). • E.E. Flanagan & S.A. Hughes’ review: arXiv:0501041. • AB’s Les Houches School Proceedings: arXiv:0709.4682. • AB & B. Sathyaprakash’s review: arXiv:1410.7832. • UMD/AEI graduate course on GW Physics & Astrophysics taught in Winter-Spring 2017: http://www.aei.mpg.de/2000472. Brief summary of Einstein equations and notations Brief summary of Einstein equations and notations (contd.) Brief summary of Einstein equations and notations (contd.) Ricci scalar: Gravitational waves: signature of dynamical spacetime • In 1916 Einstein predicted existence of gravitational waves: Linearized gravity (weak field): • Distribution of mass deforms spacetime geometry in its neighborhood. Deformations propagate away at speed of light in form of waves whose oscillations reflect temporal variation of matter distribution. Two radiative degrees of freedom (visualization: Dietrich @ AEI) Dietrich @ (visualization: Ripples in the curvature of spacetime First paper by Einstein on gravitational waves: 1916 Second paper by Einstein on gravitational waves: 1918 wrong by a factor 2! Linearization of Einstein equations • We assume there is a coordinate frame in which: Linearization of Einstein equations (contd.) Lorenz gauge can always be imposed Propagation of GW in vacuum (far from source) Imposing transverse-traceless gauge Imposing transverse-traceless gauge (contd.) Linearly polarized waves in EM & GR Circularly polarized waves in EM & GR Gravitational waves have helicity 2 Newtonian description of tidal gravity Equation of geodesic deviation Interaction of GWs with free-falling particles in local Lorentz frame Geodesic deviation equation in local-Lorentz frame (LLF) Geodesic deviation equation in local-Lorentz frame (LLF) (contd.) Geodesic deviation equation in local-Lorentz frame (LLF) (contd.) i Geodesic deviation equation in local-Lorentz frame (LLF) (contd.) KAGRA, GWs and ring of free-falling particles GWs and ring of free-falling particles (contd.) GWs and lines of force Interaction of GWs with free-falling particles using TT gauge Equivalence between TT frame and local Lorentz frame Gravitational waves in weak-field, slow velocity (at linear order in G) (assuming GW source has negligible self gravity) GW source Gravitational waves in weak-field, slow velocity (at linear order in G) (assuming GW source has negligible self gravity) GW source Gravitational waves in weak-field, slow velocity (at linear order in G) non-negligible self-gravity: Subdominant for binaries when computing quadrupole formula at leading order, but it needs to be included in conservation law, otherwise sources move along geodesic in flat spacetime We neglect Gravitational waves in weak-field, slow velocity (at linear order in G) (assuming GW source has negligible self gravity) Gravitational waves in weak-field, slow velocity (at linear order in G) (assuming GW source has negligible self gravity) Gravitational waves in weak-field, slow velocity (at linear order in G) (assuming GW source has negligible self gravity) Gravitational waves in weak-field, slow velocity (at linear order in G) Multipolar decomposition of waves (at linear order in G) • Multipolar expansion in terms of mass moments (IL) and mass current moments (JL) of source: D can’t oscillate can’t oscillate can’t oscillate source GI GI˙ GI¨ GJ˙ GJ¨ h 0 + 1 + 2 + 1 + 2 + ⇠ c2D c3D c4D c4D c5D ··· • EM & GR: electric dipole moment & mass dipole moment I : d = m x d˙ = m x = P conservation of linear 1 i i ) i i momentum i i X X • EM & GR: magnetic dipole moment & current dipole moment conservation of J1 : µ = mixi x˙ i = L ⇥ angular momentum i X The two LIGO detectors & the Virgo detector LIGO in Hanford, WA (Abbott et al. PRL 116 (2016) 061102) b) Test Mass H1 10 ms light travel time = 4 km y L a) L1 Virgo in Pisa, Italy Test Mass Power Beam L = 4 km Recycling Splitter x Laser 20 W 100 kW Circulating Power Source Test Test Mass Mass Signal Recycling Photodetector LIGO/Virgo measure (tiny) relative changes in separation of mirrors (phase shifts of light at beamsplitter of 10-9 rad!) How LIGO/Virgo work LIGO Scientific Collaboration A glimpse inside the LIGO facility LIGO Scientific Collaboration Typical noises in ground-based gravitational-wave detectors Evolution of sensitivity from Enhanced to Advanced LIGO (O1) (Martynov et al. arXiv:1604.00439) Advanced Virgo joined Advanced LIGOs on August 1, 2017 (Abbott et al. arXiv:1709.09660) 20 10− Virgo Hanford Livingston 21 10− Hz) p 22 10− Strain (1/ 23 10− 100 1000 Frequency (Hz).
Load more

Recommended publications
  • Measurement of the Speed of Gravity
    Measurement of the Speed of Gravity Yin Zhu Agriculture Department of Hubei Province, Wuhan, China Abstract From the Liénard-Wiechert potential in both the gravitational field and the electromagnetic field, it is shown that the speed of propagation of the gravitational field (waves) can be tested by comparing the measured speed of gravitational force with the measured speed of Coulomb force. PACS: 04.20.Cv; 04.30.Nk; 04.80.Cc Fomalont and Kopeikin [1] in 2002 claimed that to 20% accuracy they confirmed that the speed of gravity is equal to the speed of light in vacuum. Their work was immediately contradicted by Will [2] and other several physicists. [3-7] Fomalont and Kopeikin [1] accepted that their measurement is not sufficiently accurate to detect terms of order , which can experimentally distinguish Kopeikin interpretation from Will interpretation. Fomalont et al [8] reported their measurements in 2009 and claimed that these measurements are more accurate than the 2002 VLBA experiment [1], but did not point out whether the terms of order have been detected. Within the post-Newtonian framework, several metric theories have studied the radiation and propagation of gravitational waves. [9] For example, in the Rosen bi-metric theory, [10] the difference between the speed of gravity and the speed of light could be tested by comparing the arrival times of a gravitational wave and an electromagnetic wave from the same event: a supernova. Hulse and Taylor [11] showed the indirect evidence for gravitational radiation. However, the gravitational waves themselves have not yet been detected directly. [12] In electrodynamics the speed of electromagnetic waves appears in Maxwell equations as c = √휇0휀0, no such constant appears in any theory of gravity.
    [Show full text]
  • A Brief History of Gravitational Waves
    universe Review A Brief History of Gravitational Waves Jorge L. Cervantes-Cota 1, Salvador Galindo-Uribarri 1 and George F. Smoot 2,3,4,* 1 Department of Physics, National Institute for Nuclear Research, Km 36.5 Carretera Mexico-Toluca, Ocoyoacac, C.P. 52750 Mexico, Mexico; [email protected] (J.L.C.-C.); [email protected] (S.G.-U.) 2 Helmut and Ana Pao Sohmen Professor at Large, Institute for Advanced Study, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, 999077 Hong Kong, China 3 Université Sorbonne Paris Cité, Laboratoire APC-PCCP, Université Paris Diderot, 10 rue Alice Domon et Leonie Duquet, 75205 Paris Cedex 13, France 4 Department of Physics and LBNL, University of California; MS Bldg 50-5505 LBNL, 1 Cyclotron Road Berkeley, 94720 CA, USA * Correspondence: [email protected]; Tel.:+1-510-486-5505 Academic Editors: Lorenzo Iorio and Elias C. Vagenas Received: 21 July 2016; Accepted: 2 September 2016; Published: 13 September 2016 Abstract: This review describes the discovery of gravitational waves. We recount the journey of predicting and finding those waves, since its beginning in the early twentieth century, their prediction by Einstein in 1916, theoretical and experimental blunders, efforts towards their detection, and finally the subsequent successful discovery. Keywords: gravitational waves; General Relativity; LIGO; Einstein; strong-field gravity; binary black holes 1. Introduction Einstein’s General Theory of Relativity, published in November 1915, led to the prediction of the existence of gravitational waves that would be so faint and their interaction with matter so weak that Einstein himself wondered if they could ever be discovered.
    [Show full text]
  • Gravitational Waves from Supernova Core Collapse Outline Max Planck Institute for Astrophysics, Garching, Germany
    Gravitational Waves from Supernova Core Collapse Outline Max Planck Institute for Astrophysics, Garching, Germany Harald Dimmelmeier [email protected] Gravitational Waves from Supernova Core Collapse: What could the Signal tell us? Work done at the MPA in Garching Dimmelmeier, Font, M¨uller, Astron. Astrophys., 388, 917{935 (2002), astro-ph/0204288 Dimmelmeier, Font, M¨uller, Astron. Astrophys., 393, 523{542 (2002), astro-ph/0204289 Source Simulation Focus Session, Center for Gravitational Wave Physics, Penn State University, 2002 Gravitational Waves from Supernova Core Collapse Max Planck Institute for Astrophysics, Garching, Germany Motivation Physics of Core Collapse Supernovæ Physical model of core collapse supernova: Massive progenitor star (Mprogenitor 10 30M ) develops an iron core (Mcore 1:5M ). • ≈ − ≈ This approximate 4/3-polytrope becomes unstable and collapses (Tcollapse 100 ms). • ≈ During collapse, neutrinos are practically trapped and core contracts adiabatically. • At supernuclear density, hot proto-neutron star forms (EoS of matter stiffens bounce). • ) During bounce, gravitational waves are emitted; they are unimportant for collapse dynamics. • Hydrodynamic shock propagates from sonic sphere outward, but stalls at Rstall 300 km. • ≈ Collapse energy is released by emission of neutrinos (Tν 1 s). • ≈ Proto-neutron subsequently cools, possibly accretes matter, and shrinks to final neutron star. • Neutrinos deposit energy behind stalled shock and revive it (delayed explosion mechanism). • Shock wave propagates through
    [Show full text]
  • A Brief History of Gravitational Waves
    Review A Brief History of Gravitational Waves Jorge L. Cervantes-Cota 1, Salvador Galindo-Uribarri 1 and George F. Smoot 2,3,4,* 1 Department of Physics, National Institute for Nuclear Research, Km 36.5 Carretera Mexico-Toluca, Ocoyoacac, Mexico State C.P.52750, Mexico; [email protected] (J.L.C.-C.); [email protected] (S.G.-U.) 2 Helmut and Ana Pao Sohmen Professor at Large, Institute for Advanced Study, Hong Kong University of Science and Technology, Clear Water Bay, 999077 Kowloon, Hong Kong, China. 3 Université Sorbonne Paris Cité, Laboratoire APC-PCCP, Université Paris Diderot, 10 rue Alice Domon et Leonie Duquet 75205 Paris Cedex 13, France. 4 Department of Physics and LBNL, University of California; MS Bldg 50-5505 LBNL, 1 Cyclotron Road Berkeley, CA 94720, USA. * Correspondence: [email protected]; Tel.:+1-510-486-5505 Abstract: This review describes the discovery of gravitational waves. We recount the journey of predicting and finding those waves, since its beginning in the early twentieth century, their prediction by Einstein in 1916, theoretical and experimental blunders, efforts towards their detection, and finally the subsequent successful discovery. Keywords: gravitational waves; General Relativity; LIGO; Einstein; strong-field gravity; binary black holes 1. Introduction Einstein’s General Theory of Relativity, published in November 1915, led to the prediction of the existence of gravitational waves that would be so faint and their interaction with matter so weak that Einstein himself wondered if they could ever be discovered. Even if they were detectable, Einstein also wondered if they would ever be useful enough for use in science.
    [Show full text]
  • Gravitational Waves and Core-Collapse Supernovae
    Gravitational waves and core-collapse supernovae G.S. Bisnovatyi-Kogan(1,2), S.G. Moiseenko(1) (1)Space Research Institute, Profsoyznaya str/ 84/32, Moscow 117997, Russia (2)National Research Nuclear University MEPhI, Kashirskoe shosse 32,115409 Moscow, Russia Abstract. A mechanism of formation of gravitational waves in 1. Introduction the Universe is considered for a nonspherical collapse of matter. Nonspherical collapse results are presented for a uniform spher- On February 11, 2016, LIGO (Laser Interferometric Gravita- oid of dust and a finite-entropy spheroid. Numerical simulation tional-wave Observatory) in the USA with great fanfare results on core-collapse supernova explosions are presented for announced the registration of a gravitational wave (GW) the neutrino and magneto-rotational models. These results are signal on September 14, 2015 [1]. A fantastic coincidence is used to estimate the dimensionless amplitude of the gravita- that the discovery was made exactly 100 years after the tional wave with a frequency m 1300 Hz, radiated during the prediction of GWs by Albert Einstein on the basis of his collapse of the rotating core of a pre-supernova with a mass of theory of General Relativity (GR) (the theory of space and 1:2 M (calculated by the authors in 2D). This estimate agrees time). A detailed discussion of the results of this experiment well with many other calculations (presented in this paper) that and related problems can be found in [2±6]. have been done in 2D and 3D settings and which rely on more Gravitational waves can be emitted by binary stars due to exact and sophisticated calculations of the gravitational wave their relative motion or by collapsing nonspherical bodies.
    [Show full text]
  • Gravitational Wave Echoes from Black Hole Area Quantization
    Prepared for submission to JCAP Gravitational wave echoes from black hole area quantization Vitor Cardoso,a;b Valentino F. Foit,c Matthew Klebanc aCentro de Astrofísica e Gravitação - CENTRA, Departamento de Física Instituto Superior Técnico - IST, Universidade de Lisboa, Lisboa, Portugal bTheoretical Physics Department, CERN 1 Esplanade des Particules, Geneva 23, CH-1211, Switzerland cCenter for Cosmology and Particle Physics New York University, New York, USA E-mail: [email protected], [email protected], [email protected] Abstract. Gravitational-wave astronomy has the potential to substantially advance our knowledge of the cosmos, from the most powerful astrophysical engines to the initial stages of our universe. Gravitational waves also carry information about the nature of black holes. Here we investigate the potential of gravitational-wave detectors to test a proposal by Beken- stein and Mukhanov that the area of black hole horizons is quantized in units of the Planck area. Our results indicate that this quantization could have a potentially observable effect on the classical gravitational wave signals received by detectors. In particular, we find distorted gravitational-wave “echoes” in the post-merger waveform describing the inspiral and merger of two black holes. These echoes have a specific frequency content that is characteristic of black hole horizon area quantization. arXiv:1902.10164v1 [hep-th] 26 Feb 2019 Contents 1 Introduction1 1.1 Quantization of black hole area1 1.2 Imprints on classical observables2 1.2.1 Gravitational-wave
    [Show full text]
  • Einstein's Discovery of Gravitational Waves 1916-1918
    1 Einstein’s Discovery of Gravitational Waves 1916-1918 Galina Weinstein 12/2/16 In his 1916 ground-breaking general relativity paper Einstein had imposed a restrictive coordinate condition; his field equations were valid for a system –g = 1. Later, Einstein published a paper on gravitational waves. The solution presented in this paper did not satisfy the above restrictive condition. In his gravitational waves paper, Einstein concluded that gravitational fields propagate at the speed of light. The solution is the Minkowski flat metric plus a small disturbance propagating in a flat space-time. Einstein calculated the small deviation from Minkowski metric in a manner analogous to that of retarded potentials in electrodynamics. However, in obtaining the above derivation, Einstein made a mathematical error. This error caused him to obtain three different types of waves compatible with his approximate field equations: longitudinal waves, transverse waves and a new type of wave. Einstein added an Addendum in which he suggested that in a system –g = 1 only waves of the third type occur and these waves transport energy. He became obsessed with his system –g = 1. Einstein’s colleagues demonstrated to him that in the coordinate system –g = 1 the gravitational wave of a mass point carry no energy, but Einstein tried to persuade them that he had actually not made a mistake in his gravitational waves paper. Einstein, however, eventually accepted his colleagues results and dropped the restrictive condition –g = 1. This finally led him to discover plane transverse gravitational waves. Already in 1913, at the eighty-fifth congress of the German Natural Scientists and Physicists in Vienna, Einstein started to think about gravitational waves when he worked on the Entwurf theory.
    [Show full text]
  • Dense Nuclear Matter and Gravitational Waves Alex Nielsen Quo Vadis QCD Stavanger, Norway Wed 2Nd October 2019 Image Credit: Norbert Wex
    Dense nuclear matter and gravitational waves Alex Nielsen Quo Vadis QCD Stavanger, Norway Wed 2nd October 2019 Image Credit: Norbert Wex Neutron star radius is not directly measured in pulsars, X-ray binaries or gravitational waves, but is dependent on the matter Equation of State LIGO-Virgo result for gravitational wave event GW170817 Fig 3, LVC, PRL121, (2018) 161101 Assumptions in fitting tidal parameters ● Event is an astrophysical gravitational wave event ● Event is two neutron stars ● Event occurs exactly at the location of optical counterpart ● Both spins are low, consistent with observed galactic binaries ● Both neutron stars have the same equation of state ● GW detector noise is Gaussian, de-glitching of L1 is successful ● PhenomPNRT waveform model is accurate in inspiral phase Gravitational wave detectors (this one in Italy) Image Credit:The Virgo Collaboration Notable gravitational wave events (so far) • GW150914 Binary Black Hole (BBH) • GW170817 Binary Neutron Star (BNS) Image Credit: NASA/Dana Berry Multi-messenger astronomy, 3,677 authors... GW and EM observations of GW170817 (no neutrinos or cosmic rays seen) Fig 2, ApJL848, (2017) L12 “But, as critics have pointed out correctly, the LIGO alert for this event came 40 minutes after NASA’s gamma-ray alert. For this reason, the event cannot be used as an independent GW170817 timeline confirmation of LIGO’s detection capacity.” –Hossenfelder, 4 Sep 2019 ● 12 41:04 GstLAL automatic alert of single trigger in H1 ● 12 41:06 onboard GRB trigger on GBM ∶ ● +~15 mins Rapid Response
    [Show full text]
  • LIGO Educator's Guide
    Direct Observation of Gravitational Waves Educator’s Guide Direct Observation of Gravitational Waves Educator’s Guide http://www.ligo.org Content 3 Introduction 4 Background 4 Gravitational Waves as Signals from the Universe 5 Gravity from Newton to Einstein 8 Gravitational Waves 10 The Direct Observation of Gravitational Waves by LIGO 13 Black Holes 14 Activities 14 • Activity 1 - Coalescing Black Holes 16 • Activity 2 - Warping of Spacetime 18 Next Generation Science Standards 19 Appendix A - Glossary 20 Appendix B - Resources 21 Appendix C - Purchasing Information LIGO Educator’s Guide — This guide was written by Kevin McLin, Carolyn Peruta and Lynn Cominsky. Layout and Design by Aurore Simonnet. SSU Education and Public Outreach Group, Sonoma State University, Rohnert Park, CA – http://epo.sonoma.edu We gratefully acknowledge comments and review by Beverly Berger, Joey Key, William Katzman and Dale Ingram. This work was supported by a supplement to NSF PHY-1404215. Updates may be downloaded from https://dcc.ligo.org/LIGO-P1600015 Introduction On September 14, 2015, the Laser Interferometer Gravitational-wave Observatory (LIGO) received the first confirmed gravitational wave signals. Now known as GW150914 (for the date on which the signals were received in 2015, 9th month, day 14), the event represents the coalescence of two black holes that were previously in mutual orbit. LIGO’s exciting discovery provides direct evidence of what is arguably the last major unconfirmed prediction of Einstein’s General Theory of Relativity. This Educator’s Guide provides a brief introduction to LIGO and to gravitational waves, along with two simple demonstration activities that you can do in your classroom to engage your students in understanding LIGO’s discovery.
    [Show full text]
  • Astro2020 Science White Paper Probing the Origin of Our Universe Through Cosmic Microwave Background Constraints on Gravitational Waves
    Astro2020 Science White Paper Probing the origin of our Universe through cosmic microwave background constraints on gravitational waves Thematic Areas: Planetary Systems Star and Planet Formation Formation and Evolution of Compact Objects X Cosmology and Fundamental Physics Stars and Stellar Evolution Resolved Stellar Populations and their Environments Galaxy Evolution Multi-Messenger Astronomy and Astrophysics Principal Author: Name: Sarah Shandera Institution: The Pennsylvania State University Email: [email protected] Phone: (814)863-9595 Co-authors: Peter Adshead (U. Illinois), Mustafa Amin (Rice University), Emanuela Dimastrogiovanni (University of New South Wales), Cora Dvorkin (Harvard University), Richard Easther (University of Auckland), Matteo Fasiello (Institute of Cosmology and Gravitation, University of Portsmouth), Raphael Flauger (University of California, San Diego), John T. Giblin, Jr (Kenyon College), Shaul Hanany (University of Minnesota), Lloyd Knox (Univerisity of California, Davis), Eugene Lim (King’s College London), Liam McAllister (Cornell University), Joel Meyers (Southern Methodist University), Marco Peloso (University of Padova, and INFN, Sezione di Padova), Graca Rocha (Jet Propulsion Laboratory), Maresuke Shiraishi (National Institute of Technology, Kagawa College), Lorenzo Sorbo (University of Massachusetts, Amherst), Scott Watson (Syracuse University) Endorsers: Zeeshan Ahmed1, David Alonso2, Robert Armstrong3, Mario Ballardini4, Darcy Barron5, Nicholas Battaglia6, Daniel Baumann7;8, Charles Bennett9,
    [Show full text]
  • Stealth Chaos Due to Frame-Dragging
    Stealth Chaos due to Frame-Dragging Andr´esF. Gutierrez1 Alejandro C´ardenas-Avenda~no2 3, Nicol´asYunes3 and Leonardo A. Pach´on1 1 Grupo de F´ısicaTe´oricay Matem´aticaAplicada, Instituto de F´ısica,Facultad de Ciencias Exactas y Naturales, Universidad de Antioquia, Medell´ın,Colombia. 2 Programa de Matem´atica,Fundaci´onUniversitaria Konrad Lorenz, 110231 Bogot´a, Colombia. 3 Illinois Center for Advanced Studies of the Universe, Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA. Abstract. While the geodesic motion around a Kerr black hole is fully integrable and therefore regular, numerical explorations of the phase-space around other spacetime configurations, with a different multipolar structure, have displayed chaotic features. In most of these solutions, the role of the purely general relativistic effect of frame-dragging in chaos has eluded a definite answer. In this work, we show that, when considering neutral test particles around a family of stationary axially-symmetric analytical exact solution to the Einstein-Maxwell field equations, frame-dragging (as captured through spacetime vorticity)is capable of reconstructing KAM-tori from initially highly chaotic configurations. We study this reconstruction by isolating the contribution of the spacetime vorticity scalar to the dynamics, and exemplify our findings by computing rotation curves and the dimensionality of phase-space. Since signatures of chaotic dynamics in gravitational waves have been suggested as a way to test general relativity in the strong-field regime, we have computed gravitational waveforms using the semi- relativistic approximation and studied the frequency content of the gravitational wave spectrum. If this mechanism is generic, chaos suppression by frame-dragging may undermine present proposals to verify the hypothesis of the no-hair theorems and the validity of general relativity.
    [Show full text]
  • Gravitational Wave Friction in Light of GW170817 and GW190521
    Gravitational wave friction in light of GW170817 and GW190521. C. Karathanasis, Institut de Fisica d'Altes Energies (IFAE) On behalf of S.Mastrogiovanni, L. Haegel, I. Hernadez, D. Steer Published in Journal of Cosmology and Astroparticle Physics, Volume 2021, February 2021, Paper link Iberian Meeting, June 2021 1 Goal of the paper ● We use the gravitational wave (GW) events GW170817 and GW190521, together with their proposed electromagnetic counterparts, to constrain cosmological parameters and theories of gravity beyond General Relativity (GR). ● We consider time-varying Planck mass, large extra-dimensions and a phenomenological parametrization covering several beyond-GR theories. ● In all three cases, this introduces a friction term into the GW propagation equation, effectively modifying the GW luminosity distance. 2 Christos K. - Gravitational wave friction in light of GW170817 and GW190521. Introduction - GW ● GR: gravity is merely an effect caused by the curvature of spacetime. Field equations of GR: Rμ ν−(1/2)gμ ν R=Tμ ν where: • R μ ν the Ricci curvature tensor • g μ ν the metric of spacetime • R the Ricci scalar • T μ ν the energy-momentum tensor ● Einstein solved those and predicted (1916) the existence of disturbances in the curvature of spacetime that propagate as waves, called gravitational waves. ● Most promising sources of GW: Compact Binaries Coalescence (CBC) Binary Black Holes (BBH) Binary Neutron Star (BNS) Neutron Star Black Hole binary (NSBH) ● The metric of spacetime in case of a CBC, and sufficiently far away from it, is: ( B) gμ ν=gμ ν +hμ ν (B) where g μ ν is the metric of the background and h μ ν is the change caused by the GW.
    [Show full text]