Gravitational waves

FSU Jena, SS 2021

Lecture period: 12.04.2021 - 16.07.2021

Last updated: 13.03.2021

Lectures will be online using Zoom

Topics

• Weak field limit of GR
  • Weak-field equations
  • Solution for static sources
  • Solution for stationary sources
• Waves on flat background
  • Propagation of GWs on flat background
  • Interaction with test-masses
  • Sources of GW: quadrupole formula
• GW energy
  • Energy og GW in lienarized GR
  • Short-wave approximation
  • Isaacson tensor
• Multipolar expansion
  • Beyond the quadrupole formula
  • Multipolar expansion for scalar fields
  • STF expansion
  • Tensor spherical harmonics
• The post-Newtonian approximation
  • PN expansion of Einstein equations
  • Conservative dynamics
  • PN approach to radiation reaction
• Linearization around black holes
  • Regge-Wheeler-Zerilli equation
  • RWZ potential and black hole quasi-normal modes (ringdown)
  • Radial infall of David-Ruffini-Tiomno
• Effective-one-body description of the general-relativistic 2-body problem
  • Relative motion and Schwarzschild Hamiltonian
  • Mapping the conservative dynamics
  • Resummation aspects and waveform generation
• Strong, self-gravity and high-velocities source
  • The binary-black hole merger waveform
  • Kicks (Fouchet formula, and numerical relativity predictions)
  • Gravitational collapse and signals from CCSN
• Detection and data-analysis
  • Noise spectral density
  • Antenna pattern
  • Match-filtering & Bayesian methods

Books

• M.Maggiore, “Gravitational Waves, Vol.1: Theory and Experiments”, Oxford University Press, 2008.
• M.Maggiore, “Gravitational Waves, Vol.2: Astrophysics and Cosmology”, Oxford University Press, 2018.
• S.Chandrasekhar, “The Mathematical Theory of Black Holes”, Oxford University Press, 1983.
• Y.Choquet-Bruhat, “General Relativity and the Einstein Equations”, Oxford Mathematical Monographs, 2009.
• Y.Choquet-Bruhat, “Introduction to General Relativity, Black Holes, and Cosmology”, Oxford Mathematical Monographs, 2015.

Reviews

• L.Blanchet living review on post-Newtonian methods
• E.Berti et al review on quasi-normal modes of black holes
• T.Damour 1974: the discovery of the first binary pulsar
• K.Kokkotas and B.G.Schmidt living review on quasi-normal modes of stars and black holes
• P.Jaranowski and A.Krolak living review on GW data analysis
• C.Will The Confrontation between General Relativity and Experiment
• P.Nollert Quasinormal modes: the characteristic `sound’ of black holes and neutron stars
• M.Pitkin et al living review on GW interferometers
• D.Radice et al. The Dynamics of Binary Neutron Star Mergers and of GW170817
• B.S.Sathyaprakash and B.F.Schutz living review on GW

Lecture notes

• A.Buonanno Lectures on GW
• W.Del Pozzo Lectures on GW data analysis
• V.Ferrari Lectures on GW and compact objects
• E.Flanagan & Hughes The basics of gravitational wave theory
• ICTS Summer School on Gravitational-Wave Astronomy
• M.Hendry Lectures on GW
• J.Novak Lectures on GR and GW
• P.Pani Lectures on black hole perturbation theory
• E.Poisson Lectures on post-Newtonian methods
• G.Schäfer, P.Jaranowski Living review on Hamiltonian formulation

Suggested articles

• Einstein (1916) and (1918) (See also A.Einstein in Annalen der Physik)
• Regge & Wheeler (1957) Stability of a Schwarzschild Singularity
• Brill and Hartle (1963) Method of the Self-Consistent Field in General Relativity
• Peters & Mathews (1963) Gravitational Radiation from Point Masses in a Keplerian Orbit
• Isaacson PhD thesis (1967)
• Isaacson (1968) Gravitational Radiation in the Limit of High Frequency: Nonlinear Terms and the Effective Stress Tensor
• Vishveshwara PhD thesis (1968)
• Vishveshwara (1970) Scattering of Gravitational Radiation by a Schwarzschild Black-hole
• Chandrasekhar & Esposito Farese (1970) The 2½-post-Newtonian Equations of Hydrodynamics and Radiation Reaction in General Relativity
• Press&Thorne (1972) Gravitational-wave Astronomy
• David, Ruffini & Tiomno (1972) Pulses of Gravitational Radiation of a Particle Falling Radially into a Schwarzschild Black Hole
• Chandrasekhar & Detweiler (1975) The quasi-normal modes of the Schwarzschild black hole
• Damour (1983) Gravitational Radiation Reaction in the Binary Pulsar and the Quadrupole-Formula Controversy
• Leaver (1986) Analytic representation for the quasi-normal modes of Kerr black holes
• Blanchet & Damour (1986) Radiative Gravitational Fields in General Relativity
• Babak & Grishchuk (1999) The Energy-Momentum Tensor for the Gravitational Field
• Pretorius (2005) First binary black hole merger in numerical relativity
• Martel & Poisson (2005) Gravitational perturbations of the Schwarzschild spacetime: A practical covariant andgauge-invariant formalism
• Maggiore (2007) Mechanical interpretation of the spectrum of black hole quasinormal modes

Papers about pulsars and LIGO-Virgo observations

• Hulse-Taylor PSR B1913+16 measurement
  • 1975
  • 1993 Nobel prize, press release
  • 2010
  • 2016
• LIGO-Virgo measurements
  • Crab pulsar spindown limit (2008)
  • Black hole merger (2015)
  • Black hole merger, three detectors observations (2017)
  • Binary neutron star inspiral (2017)
  • 2017 Nobel prize, press release

Resources on the web

Videos

• T.Damour’s YouTube lectures
  • Part 1/4
  • Part 2/4
  • Part 3/4
  • Part 4/4
• C.Will’s YouTube lectures/talks
  • Lectures on Newtonian, post-Newtonian, relativistic gravity
  • Was Einstein right? A centennial assessment
• E.Poisson’s YouTube lectures
  • Black Hole Perturbation Theory - Lecture 1
• M.Kramer Nearly 100 years after General Relativity: Was Einstein right? (Pulsars tests)
• Gravitational Wave first detection, Press conference on February 11, 2016
• Gravity Probe B press conference

Data/software/msc

• Berti’s ringdown page
• Gravitational Wave Open Science Center
• Guth notes on STF and multipolaar expansion
• Caltech’s LIGO website
• NIST Digital Library of Mathematical Functions
• xPert Mathematica package for computer algebra for metric perturbation theory. See also this paper
• Material put together by N.K.Johnson-MacDaniel for the 2011-2012 GW courses at Jena
• Virgo website

Course material

Lecture notes:

• Gravitational waves
• Theory of Probability

Exercises

Tutor: M.Breschi

• Sheet n.1: Inertia tensor
• Sheet n.2: Linearized GR
• Sheet n.3: No-stress source
• Sheet n.4: Geodesic deviation
• Sheet n.5: Circular binary system
• Sheet n.6: Energy of a binary system
• Sheet n.7: Eccentric binary system
• Sheet n.8: STF tensor vs. Multipoles
• Sheet n.9: Stationary phase approximation

Python course

• Introduction

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