Gravitational Wave Tests of General Relativity with Ground-Based Detectors and Pulsar Timing Arrays

Abstract

This review is focused on tests of Einstein's theory of General Relativity with gravitational waves that are detectable by ground-based interferometers and pulsar timing experiments. Einstein's theory has been greatly constrained in the quasi-linear, quasi-stationary regime, where gravity is weak and velocities are small. Gravitational waves will allow us to probe a complimentary, yet previously unexplored regime: the non-linear and dynamical strong-field regime. Such a regime is, for example, applicable to compact binaries coalescing, where characteristic velocities can reach fifty percent the speed of light and compactnesses can reach a half. This review begins with the theoretical basis and the predicted gravitational wave observables of modified gravity theories. The review continues with a brief description of the detectors, including both gravitational wave interferometers and pulsar timing arrays, leading to a discussion of the data analysis formalism that is applicable for such tests. The review ends with a discussion of gravitational wave tests for compact binary systems.

arXiv comment123 pages, 5 figures, replaced with version accepted for publication in the Living Reviews in Relativity

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• Perturbations of spinning black holes beyond General Relativity: Modified Teukolsky equation
• The Emergence of Structure in the Binary Black Hole Mass Distribution
• Search for intermediate mass black hole binaries in the third observing run of Advanced LIGO and Advanced Virgo
• The Initial Value Formulation of Dynamical Chern-Simons Gravity
• Rotating regular black holes in conformal massive gravity
• A standard siren measurement of the Hubble constant using gravitational wave events from the first three LIGO/Virgo observing runs and the DESI Legacy Survey
• Polarizations of Gravitational Waves in Horndeski Theory
• Fixing extensions to General Relativity in the non-linear regime
• Quasi-normal modes of black holes in Horndeski gravity
• Overtones or higher harmonics? Prospects for testing the no-hair theorem with gravitational wave detections
• Constraints on ultralight scalar dark matter from pulsar timing
• Relaxations of perturbations of spacetimes in general relativity coupled to nonlinear electrodynamics
• Relativistic stars in scalar-tensor theories with disformal coupling
• Parameterized tests of the strong-field dynamics of general relativity using gravitational wave signals from coalescing binary black holes: Fast likelihood calculations and sensitivity of the method
• Gravitational Waves Probes of Parity Violation in Compact Binary Coalescence
• Black Hole Shadow as a Test of General Relativity: Quadratic Gravity
• Viewpoint: The First Sounds of Merging Black Holes
• Post-Kerr black hole spectroscopy
• Exploring New Physics Frontiers Through Numerical Relativity
• Search for intermediate mass black hole binaries in the first and second observing runs of the Advanced LIGO and Virgo network
• Nonlinear studies of binary black hole mergers in Einstein-scalar-Gauss-Bonnet gravity
• Neutron Star Mergers and How to Study Them
• Probing the Internal Composition of Neutron Stars with Gravitational Waves
• New pulsar limit on local Lorentz invariance violation of gravity in the standard-model extension
• Three-Hair Relations for Rotating Stars: Nonrelativistic Limit
• Gravitational radiation from compact binary systems in screened modified gravity
• Measuring Speed of Gravitational Waves by Observations of Photons and Neutrinos from Compact Binary Mergers and Supernovae
• Systematic bias on parameterized tests of general relativity due to neglect of orbital eccentricity
• The NANOGrav 12.5-year data set: Search for Non-Einsteinian Polarization Modes in theGravitational-Wave Background
• Pulsar-timing arrays, astrometry, and gravitational waves
• Enhancing modified gravity detection from gravitational-wave observations using the Parametrized ringdown spin expansion coefficients formalism
• Listening to the Universe with Next Generation Ground-Based Gravitational-Wave Detectors
• Spin-induced dynamical scalarization, de-scalarization and stealthness in scalar-Gauss-Bonnet gravity during black hole coalescence
• Exotic compact objects with soft hair
• Testing conformal gravity with the supermassive black hole in 1H0707-495
• Testing conformal gravity with astrophysical black holes
• The Effect of Cosmological Evolution on Solar System Constraints and on the Scalarization of Neutron Stars in Massless Scalar-Tensor Theories
• Nonlinear/non-iterative treatment of EFT-motivated gravity
• Probing Gravitational Parity Violation with Gravitational Waves from Stellar-mass Black Hole Binaries
• Constraining the Polarization Content of Gravitational Waves with Astrometry
• Constraining alternative theories of gravity using pulsar timing arrays
• Bounding Alternative Theories of Gravity with Multi-Band GW Observations
• Testing the multipole structure of compact binaries using gravitational wave observations
• The multipolar structure of fuzzballs
• Towards the nonlinear regime in extensions to GR: assessing possible options
• Cosmological perturbation effects on gravitational-wave luminosity distance estimates
• Asymptotically flat, parameterized black hole metric preserving Kerr symmetries
• Towards numerical relativity in scalar Gauss-Bonnet gravity: 3+1 decomposition beyond the small-coupling limit
• Gravitational-wave versus X-ray tests of strong-field gravity
• Modeling dynamical scalarization with a resummed post-Newtonian expansion
• Measuring the propagation speed of gravitational waves with LISA
• Gravitational-Wave Implications for the Parity Symmetry of Gravity at GeV Scale
• The Transient Gravitational-Wave Sky
• Gravity experiments with radio pulsars
• Binary Pulsar constraints on massless scalar-tensor theories using Bayesian statistics
• Numerical simulations of stellar collapse in scalar-tensor theories of gravity
• A Parametrized post-Einsteinian Framework for Gravitational Wave Bursts
• Multi-band gravitational wave tests of general relativity
• Compact objects in Horndeski gravity
• Quasi-normal mode frequencies and gravitational perturbations of black holes with any subextremal spin in modified gravity through METRICS: the scalar-Gauss-Bonnet gravity case
• Scalar perturbations of nonsingular nonrotating black holes in conformal gravity
• Tests of gravitational symmetries with radio pulsars
• Detection and Parameter Estimation of Gravitational Waves from Compact Binary Inspirals with Analytical Double-Precessing Templates
• Adding eccentricity to quasicircular binary-black-hole waveform models
• Tests of general relativity using multiband observations of intermediate mass binary black hole mergers
• A study of the strong gravity region of the black hole in GS 1354-645
• Gravitational Wave Polarizations in $f(R)$ Gravity and Scalar-Tensor Theory
• Extremal Black Holes in Dynamical Chern-Simons Gravity
• Gravitational Wave Interference via Gravitational Lensing: Measurements of Luminosity Distance, Lens Mass, and Cosmological Parameters
• Constraints on the binary black hole nature of GW151226 and GW170608 from the measurement of spin-induced quadrupole moments
• Higher-order theories of gravity: diagnosis, extraction and reformulation via non-metric extra degrees of freedom
• Frequency response of space-based interferometric gravitational-wave detectors
• Tests of the Kerr hypothesis with GRS 1915+105 using different RELXILL flavors
• Chirality of the gravitational-wave background and pulsar-timing arrays
• Spin-induced deformations and tests of binary black hole nature using third-generation detectors
• Parametrized tests of post-Newtonian theory using principal component analysis
• Numerical relativity for Horndeski gravity
• Gravitational lensing of a Schwarzschild-like black hole in Kalb-Ramond gravity
• Testing general relativity with gravitational-wave catalogs: the insidious nature of waveform systematics
• The search for anisotropy in the gravitational-wave background with pulsar-timing arrays
• Testing Einstein-dilaton-Gauss-Bonnet gravity from the reflection spectrum of accreting black holes
• Comparison of post-Newtonian mode amplitudes with numerical relativity simulations of binary black holes
• Iron K$\alpha$ line of boson stars
• Black hole spectroscopy horizons for current and future gravitational wave detectors
• The Lunar Gravitational-wave Antenna: Mission Studies and Science Case
• How well can ultracompact bodies imitate black hole ringdowns?
• Spectroscopic analysis of stellar mass black-hole mergers in our local universe with ground-based gravitational wave detectors
• Binary pulsars as dark-matter probes
• Gravitational wave memory beyond general relativity
• Neutron Stars in Screened Modified Gravity: Chameleon vs Dilaton
• Spectral method for metric perturbations of black holes: Kerr background case in general relativity
• Testing Gravity with Black Hole Shadow Subrings
• Quasi-periodic oscillations as a tool for testing the Kerr metric: A comparison with gravitational waves and iron line
• Probing Einstein-dilaton Gauss-Bonnet Gravity with the inspiral and ringdown of gravitational waves
• Negative time delay of light by a gravitational concave lens
• Spectral Method for the Gravitational Perturbations of Black Holes: Schwarzschild Background Case
• Model-independent test of the parity symmetry of gravity with gravitational waves
• Post-Newtonian constraints on Lorentz-violating gravity theories with a MOND phenomenology
• Modelling gravitational waves from precessing black-hole binaries: Progress, challenges and prospects
• Gravitational waves in Einstein-Æther theory and generalized TeVeS theory after GW170817
• Parity violating Friedmann Universes
• Measuring stochastic gravitational-wave energy beyond general relativity
• Estimating parameters of binary black holes from gravitational-wave observations of their inspiral, merger and ringdown
• Testing general relativity with the stellar-mass black hole in LMC X-1 using the continuum-fitting method
• Probing gravity and growth of structure with gravitational waves and galaxies' peculiar velocity
• Testing the multipole structure and conservative dynamics of compact binaries using gravitational wave observations: The spinning case
• I-Love-Q Relations for Neutron Stars in dynamical Chern Simons Gravity
• Superradiance in Kerr-like black holes
• Numerical Black Hole Solutions in Modified Gravity Theories: Axial Symmetry Case
• $d+1$ formalism in Einstein-scalar-Gauss-Bonnet gravity
• Towards a framework for testing general relativity with extreme-mass-ratio-inspiral observations
• Testing the Kerr black hole hypothesis: comparison between the gravitational wave and the iron line approaches
• Square Peg in a Circular Hole: Choosing the Right Ansatz for Isolated Black Holes in Generic Gravitational Theories
• Constraining modified theories of gravity with gravitational wave stochastic background
• Investigation of the effects of non-Gaussian noise transients and their mitigation in parameterized gravitational-wave tests of general relativity
• Gravitational perturbations of a Kerr black hole in $f(R)$ gravity
• Binary White Dwarfs as Laboratories for Extreme Gravity with LISA
• Eccentricity-induced systematic error on parametrized tests of general relativity: Hierarchical Bayesian inference applied to a binary black hole population
• Petrov Type, Principal Null Directions, and Killing Tensors of Slowly-Rotating Black Holes in Quadratic Gravity
• Exact Black Hole Solutions in Modified Gravity Theories: Spherical Symmetry Case
• The exact dynamical Chern Simons metric for a spinning black hole possesses a fourth constant of motion: A Dynamical-Systems-Based Conjecture
• The multipolar structure of rotating boson stars
• Spin-orbit effects for compact binaries in scalar-tensor gravity
• Massive Black Hole Science with eLISA
• About the Kerr nature of the stellar-mass black hole in GRS 1915+105
• Constraining alternative polarization states of gravitational waves from individual black hole binaries using pulsar timing arrays
• Cosmological Evolution and Solar System Consistency of Massive Scalar-Tensor Gravity
• Convergence of Fourier-domain templates for inspiraling eccentric compact binaries
• Gravitational lensing by exotic objects
• Astrometric Effects of Gravitational Wave Backgrounds with non-Luminal Propagation Speeds
• Measuring the ringdown scalar polarization of gravitational waves in Einstein scalar Gauss-Bonnet gravity
• General constraints on Horndeski wormhole throats
• Inspiralling compact objects with generic deformations
• Study of eccentric binaries in Horndeski theory
• Linear stability of nonbidiagonal black holes in massive gravity
• Analytic charged BHs in $f(\mathcal{R})$ gravity
• Detectability of bigravity with graviton oscillations using gravitational wave observations
• Constraining the propagation speed of gravitational waves with compact binaries at cosmological distances
• Gravitational Instability of Exotic Compact Objects
• Quasinormal mode frequencies and gravitational perturbations of spinning black holes in modified gravity through METRICS: The dynamical Chern-Simons gravity case
• Scattering of point particles by black holes: gravitational radiation
• Future prospects on testing extensions to $\Lambda$CDM through the weak lensing of gravitational waves
• Ringdown of Charged Compact Objects using Membrane Paradigm
• Gaussian Processes for Glitch-robust Gravitational-wave Astronomy
• Distinguishing general relativity from Chern-Simons gravity using gravitational wave polarizations
• Black Hole Continuum Spectra as a Test of General Relativity: Quadratic Gravity
• Probing a stationary non-Gaussian background of stochastic gravitational waves with pulsar timing arrays
• Improved Constraints on Modified Gravity with Eccentric Gravitational Waves
• Black hole accretion discs and screened scalar hair
• Constraining scalarization in scalar-Gauss-Bonnet gravity through binary pulsars
• The Role of Baryon Structure in Neutron Stars
• Constraining Screened Modified Gravity by Space-borne Gravitational-wave Detectors
• The shape of Scalar Gauss-Bonnet Gravity
• Astrophysical applications of the post-Tolman-Oppenheimer-Volkoff formalism
• Numerical simulations of black hole-neutron star mergers in scalar-tensor gravity
• Constraints of general screened modified gravities from comprehensive analysis of binary pulsars
• Astrophysical black holes in screened modified gravity
• Testing the Kerr nature of intermediate-mass and supermassive black hole binaries using spin-induced multipole moment measurements
• RELXILL_NK: a relativistic reflection model for testing Einstein's gravity
• Beyond the Hellings-Downs curve: Non-Einsteinian gravitational waves in pulsar timing array correlations
• Quasinormal modes, temperatures and greybody factors of black holes in a generalized Rastall gravity theory
• Spinning compact binary dynamics and chameleon orbits
• Gravitational atoms in the braneworld scenario
• Experimental Relativity with Accretion Disk Observations
• The future of gravitational theories in the era of the gravitational wave astronomy
• Observational constraints on spinning, relativistic Bose-Einstein condensate stars
• Gravitational-wave polarizations in generic linear massive gravity and generic higher-curvature gravity
• Principles of Gravitational-Wave Detection with Pulsar Timing Arrays
• Disformal map and Petrov classification in modified gravity
• Gravitational wave constraints on Einstein-æther theory with LIGO/Virgo data
• Multi-scale Constraints on Scalar-Field couplings to Matter: The Geodetic and Frame-Dragging Effects
• Does black hole continuum spectrum signal f(R) gravity in higher dimensions?
• Black-hole spectroscopy: quasinormal modes, ringdown stability and the pseudospectrum
• Gravitational wave polarizations with different propagation speeds
• Probing Screening and the Graviton Mass with Gravitational Waves
• Geometrical origins of the Universe dark sector: string-inspired torsion and anomalies as seeds for inflation and dark matter
• Covariant Equations of Motion of Extended Bodies with Arbitrary Mass and Spin Multipoles
• Analysis of GWTC-3 with fully precessing numerical relativity surrogate models
• Constraining gravitational-wave polarizations with Taiji
• Testing the Kerr metric with X-ray Reflection Spectroscopy of Mrk 335 Suzaku data
• How Do Spherical Black Holes Grow Monopole Hair?
• Gravitational Waves in Chern-Simons-Gauss-Bonnet Gravity
• I-Love-Q to the extreme
• Review of Pulsar Timing Array for Gravitational Wave Research
• Constraining Gravity with Eccentric Gravitational Waves: Projected Upper Bounds and Model Selection
• Infinitely degenerate exact Ricci-flat solutions in f(R) gravity
• Resumming Post-Minkowskian and Post-Newtonian gravitational waveform expansions
• Probing parity-odd bispectra with anisotropies of GW $V$ modes
• Improved binary pulsar constraints on the parameterized post-Einsteinian framework
• How Do Axisymmetric Black Holes Grow Monopole and Dipole Hair?
• Gravity generated by four one-dimensional unitary gauge symmetries and the Standard Model
• Testing the Weak Equivalence Principle near black holes
• Differentially rotating scalarized neutron stars with realistic post-merger profile
• Scalar Charges and Scaling Relations in Massless Scalar-Tensor Theories
• Iron K$\alpha$ line of Kerr black holes with Proca hair
• Parametrized tests of general relativity using eccentric compact binaries
• Measuring violations of General Relativity from single gravitational wave detection by non-spinning binary systems: higher-order asymptotic analysis
• Testing the Kerr metric using X-ray reflection spectroscopy: spectral analysis of GX 339-4
• Supermassive Black Hole Tests of General Relativity with eLISA
• Dark photon bursts from compact binary systems and constraints
• Logarithmic corrections to Newtonian gravity and Large Scale Structure
• Beyond general relativity: designing a template-based search for exotic gravitational wave signals
• Parameter Estimation for Tests of General Relativity with the Astrophysical Stochastic Gravitational Wave Background
• - Gravitational Waves - A Review on the Conceptual Foundations of Gravitational Radiation
• Black holes and fundamental fields: hair, kicks and a gravitational "Magnus" effect
• Probing dark-matter effects with gravitational waves using the parameterized post-Einsteinian framework
• Charged black hole and radiating solutions in entangled relativity
• Monopolar and quadrupolar gravitational radiation from magnetically deformed neutron stars in modified gravity
• Generic EFT-motivated beyond General Relativity gravitational wave tests and their curvature dependence: from observation to interpretation
• Dark Matter-admixed Rotating White Dwarfs as Peculiar Compact Objects
• Fundamental Physics and Cosmology with TianQin
• Relativistic reflection spectra of super-spinning black holes
• The curvature dependence of gravitational-wave tests of General Relativity
• In quest of axionic hairs in quasars
• Gauge independent response of a laser interferometer to gravitational waves
• Breaking black-hole uniqueness at supermassive scales
• Einstein-Klein-Gordon system via Cauchy-characteristic evolution: Computation of memory and ringdown tail
• Strong Equivalence Principle and Gravitational Wave Polarizations in Horndeski Theory
• Observation of gravitational waves by light polarization
• The potential of advanced ground-based gravitational wave detectors to detect generic deviations from general relativity
• Improving parameter estimation accuracy with torsion-bar antennas
• Covariant constructive gravity: A step-by-step guide towards alternative theories of gravity
• Non-linear spherical collapse in tachyon models, and a comparison of collapse in tachyon and quintessence models of dark energy
• Gravitational partition function modified by super-light brane world perturbative modes
• Testing Ghasemi-Nodehi-Bambi metric parameters with quasi-periodic oscillations
• Prospects of constraining on the polarizations of gravitational waves from binary black holes using space- and ground-based detectors
• Gravitational-Wave Signatures of Nonstandard Neutrino Properties in Collapsing Stellar Cores
• Primordial scalar gravitational waves produced at the QCD phase transition due to the trace anomaly
• Gravitational-wave memory effects in the Damour-Esposito-Farèse extension of Brans-Dicke theory
• Exploring Dark Forces with Multimessenger Studies of Extreme Mass Ratio Inspirals
• Constraints on Einstein-dilaton Gauss-Bonnet gravity with Taiji
• Relativistic tidal effects in non standard Kerr space-time
• Gravitational wave oscillations in bimetric cosmology
• The Impact of Dark Matter on Gravitational Wave Detection by Space-based Interferometers
• Early-universe cosmology in Einstein-scalar-Gauss-Bonnet gravity
• Neutron stars in general relativity and scalar-tensor theory of gravity
• Inferring astrophysics and cosmology with individual compact binary coalescences and their gravitational-wave stochastic background
• Constraints on fourth order gravity from binary pulsar and gravitational waves
• Observational appearance of Kaluza-Klein black holes
• Gravitational radiation from birefringent matter dynamics
• Connecting Inflation to the NANOGrav 15-year Data Set via Massive Gravity
• Sgr A* Shadow Study with KTN Space Time and Investigation of NUT Charge Existence
• Neutron stars in the generalized SU(2) Proca theory
• Probing Fundamental Physics with Gravitational Waves
• The Response of Laser Interferometric Gravitational Wave Detectors Beyond the Eikonal Equation
• Is Gravity Actually the Curvature of Spacetime?
• Detection of gravitational waves by light perturbation
• Sub-Planckian scale and limits for $f(R)$ models
• A study for testing the Kerr metric with AGN iron line eclipses
• Ten years of extreme gravity tests of general theory of relativity with gravitational-wave observations
• Rotations of the polarization of a gravitational wave propagating in Universe
• More than the sum of its parts: combining parameterized tests of extreme gravity
• Observation of Gravitational Waves by Invariants for Electromagnetic Waves
• Cosmological Solutions for the Geometrical Scalar-Tensor with the Potential Determined by the Noether Symmetry Approach
• Gravitational wave pulse and memory effects for hairy Kiselev black hole and its analogy with Bondi-Sachs formalism
• Dynamical Chameleon Neutron Stars: stability, radial oscillations and scalar radiation in spherical symmetry
• Tests of general relativity at the fourth post-Newtonian order
• Gravitational wave from cosmic inflation in a gravity with two small four-derivative corrections
• Influence Through Mixing: Hotspots as Benchmarks for Basic Black-Hole Behaviour
• Data Analysis of Massive Gravitational Waves from Gamma Ray Bursts
• Synergy between ground and space based gravitational wave detectors for estimation of binary coalescence parameters
• Testing the Kerr black hole hypothesis with RELXILL_NK
• Gravitational waves in metric-affine bumblebee gravity
• Fundamental fields around compact objects: Massive spin-2 fields, Superradiant instabilities and Stars with dark matter cores
• Constraining scalar-tensor theories from higher harmonics with GW230529
• Gravitational waves in massive Horndeski theory with a potential
• Observations of General Relativity at strong and weak limits
• Gravitational wave memory in wormhole spacetimes
• $\kappa$-General-Relativity II: An Astrophysical Observable from a 2-Body system
• Quasinormal Modes of Extremal Reissner-Nordstrom Black Holes via Seiberg-Witten Quantization
• Dynamics of a homogeneous and isotropic space in pure cubic f(R) gravity
• Tests of scalar polarizations with multi-messenger events
• Testing general relativity with X-ray reflection spectroscopy of MCG-06-30-15
• Physics Beyond the Standard Model With Pulsar Timing Arrays
• The Unique Blazar OJ 287 and its Massive Binary Black Hole Central Engine
• Fast and Fewrious: Stochastic binary perturbations from fast compact objects
• The initial value problem for gravitational waves in conformal gravity
• Rotation-dependent $I$-Love-$Q$-$\delta M$ relations in perturbation theory