Analyzing Gravitational Waves with General Relativity
arXiv:1902.09801 · doi:10.1016/j.crhy.2019.02.004
Abstract
After a short review of prominent properties of gravitational waves and the newly born gravitational astronomy, we focus on theoretical aspects. Analytic approximation methods in general relativity have played a crucial role in the recent discoveries of gravitational waves. They are used to build theoretical template banks for searching and analyzing the signals in the ground-based detectors LIGO and Virgo, and, further ahead, space-based LISA-like detectors. In particular, the post-Newtonian approximation describes with high accuracy the early inspiral of compact binary systems, made of black holes or neutron stars. It mainly consists of extending the Einstein quadrupole formula by a series of relativistic corrections up to high order. The compact objects are modelled by point masses with spins. The practical calculations face difficult problems of divergences, which have been solved thanks to the dimensional regularization. In the last rotations before the merger, the finite size effects and the internal structure of neutron stars (notably the internal equation of state) affect the evolution of the orbit and the emission of gravitational waves. We describe these effects within a simple Newtonian model.
arXiv comment14 pages, 5 figures, Invited review article to appear in Comptes Rendus de l'Académie des Sciences (Physique)
References in corpus (55)
- Observation of Gravitational Waves from a Binary Black Hole Merger
- GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
- The Dynamics of General Relativity
- Evolution of Binary Black Hole Spacetimes
- Accurate Evolutions of Orbiting Black-Hole Binaries Without Excision
- Tidal Love numbers of neutron stars
- Effective one-body approach to general relativistic two-body dynamics
- Gravitational wave extraction from an inspiraling configuration of merging black holes
- Constraining neutron star tidal Love numbers with gravitational wave detectors
- On gravitational-wave spectroscopy of massive black holes with the space interferometer LISA
- Relativistic tidal properties of neutron stars
- Relativistic theory of tidal Love numbers
- Inspiral-merger-ringdown waveforms for black-hole binaries with non-precessing spins
- Gravitational-Radiation Damping of Compact Binary Systems to Second Post-Newtonian order
- The Last Three Minutes: Issues in Gravitational Wave Measurements of Coalescing Compact Binaries
- Matching post-Newtonian and numerical relativity waveforms: systematic errors and a new phenomenological model for non-precessing black hole binaries
- Gravitational radiation from inspiralling compact binaries completed at the third post-Newtonian order
- Systematic parameter errors in inspiraling neutron star binaries
- Nonlocal-in-time action for the fourth post-Newtonian conservative dynamics of two-body systems
- Binary Neutron Star Mergers
- Gravitational-Wave Inspiral of Compact Binary Systems to 7/2 Post-Newtonian Order
- Gravitational waves from inspiralling compact binaries: Energy loss and waveform to second--post-Newtonian order
- Effective-one-body waveforms calibrated to numerical relativity simulations: coalescence of non-spinning, equal-mass black holes
- Gravitational waves from inspiralling compact binaries: Energy flux to third post-Newtonian order
- Effective action approach to higher-order relativistic tidal interactions in binary systems and their effective one body description
- Quadratic-in-spin effects in the orbital dynamics and gravitational-wave energy flux of compact binaries at the 3PN order
- Gravitational-wave tails of tails
- Next-to-next-to-leading order spin-orbit effects in the gravitational wave flux and orbital phasing of compact binaries
- Effective-one-body waveforms calibrated to numerical relativity simulations: coalescence of non-precessing, spinning, equal-mass black holes
- High-accuracy numerical simulation of black-hole binaries: Computation of the gravitational-wave energy flux and comparisons with post-Newtonian approximants
- Fokker action of non-spinning compact binaries at the fourth post-Newtonian approximation
- Second-post-Newtonian generation of gravitational radiation
- The tail effect in gravitational radiation-reaction: time non-locality and renormalization group evolution
- On the multipole expansion of the gravitational field
- Motion in alternative theories of gravity
- Gravitational Recoil of Inspiralling Black-Hole Binaries to Second Post-Newtonian Order
- Mass, inertia and gravitation
- Gravitational Waves by a Particle in Circular Orbits around a Schwarzschild black hole -5.5 Post-Newtonian Formula-
- Energy and periastron advance of compact binaries on circular orbits at the fourth post-Newtonian order
- Ambiguity-Free Completion of the Equations of Motion of Compact Binary Systems at the Fourth Post-Newtonian Order
- The dynamics of the gravitational two-body problem at fourth post-Newtonian order and at quadratic order in the Newton constant
- Dimensional regularization of local singularities in the 4th post-Newtonian two-point-mass Hamiltonian
- Hadamard regularization of the third post-Newtonian gravitational wave generation of two point masses
- Post-Newtonian approximation for isolated systems calculated by matched asymptotic expansions
- Center-of-mass angular momentum and memory effect in asymptotically flat spacetimes
- Dynamics of compact binary systems in scalar-tensor theories: I. Equations of motion to the third post-Newtonian order
- Towards the 4th post-Newtonian Hamiltonian for two-point-mass systems
- Dimensional regularization of the IR divergences in the Fokker action of point-particle binaries at the fourth post-Newtonian order
- Computing the merger of black-hole binaries: the IBBH problem
- Next-to-leading tail-induced spin-orbit effects in the gravitational radiation flux of compact binaries
- Dynamics of compact binary systems in scalar-tensor theories: II. Center-of-mass and conserved quantities to 3PN order
- On the structure of the post-Newtonian expansion in general relativity
- Gravitational-wave tail effects to quartic non-linear order
- Flux-balance equations for linear momentum and center-of-mass position of self-gravitating post-Newtonian systems
- Spin and Center of mass comparison between the PN approach and the asymptotic formulation
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- Quasinormal Modes of Black Holes Surrounded by Dark Matter and Their Connection with the Shadow Radius
- Connection Between the Shadow Radius and Quasinormal Modes in Rotating Spacetimes
- The Science of the Einstein Telescope
- Fourth post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach
- Shadow, quasinormal modes and quasiperiodic oscillations of rotating Kaluza-Klein black holes
- Role of dense matter in tidal deformations of inspiralling neutron stars and in gravitational waveform with unified equations of state
- Comparison and application of different post-Newtonian models for inspiralling stellar-mass binary black holes with space-based GW detectors
- Field excitation in fuzzy dark matter near a strong gravitational wave source
- GW170814: Gravitational wave polarization analysis
- Off-centred force-free neutron star magnetospheres
- Eccentric Pairs: Analytic Gravitational Waves from Binary Black Holes in Elliptic Orbits
- Rising Tides: Analytic Modeling of Tidal Effects in Binary Neutron Star Mergers
- Constraining Kerr supermassive black hole properties using gravitational waves from inspiraling stellar-mass binary black holes