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A research-oriented map of the observables, theory mappings, inference methods and limitations by which gravitational-wave, gamma-ray, kilonova, afterglow and prospective neutrino data from binary neutron-star mergers constrain departures from general relativity.

Key terms

• Scalarisation — A nonlinear strong-field phenomenon in some scalar–tensor theories in which a neutron star develops an effective scalar charge, potentially abruptly during inspiral.
  It can create dipole radiation and late-inspiral or merger deviations while evading some weak-field constraints.
• Tidal deformability — The linear response of a neutron star’s multipole moments to its companion’s tidal field, commonly encoded by a Love number or dimensionless parameter Λ.
  It carries dense-matter information but is also a principal degeneracy in gravity tests using binary neutron-star inspiral phasing.
• Gravitational-wave luminosity distance — The distance inferred from gravitational-wave amplitude after accounting for source orientation and waveform parameters.
  Modified tensor damping, a varying effective Planck mass or gravitational leakage can make it differ from electromagnetic luminosity distance.
• Modified dispersion — A non-general-relativistic relation between gravitational-wave frequency and wave number that produces frequency-dependent propagation speed and phase shifts.
  Gravitational-wave phasing tests it directly; electromagnetic coincidence adds an absolute inter-messenger timing lever arm.
• Shapiro delay — Propagation-time delay accumulated by a signal traversing gravitational potentials.
  Comparing the delay for different messengers provides a route to tests of weak equivalence-principle violation.
• Hierarchical inference — A statistical framework that jointly infers event-level parameters and shared population-level parameters using multiple events.
  It is needed to avoid conflating modified gravity with equations of state, cosmological, astrophysical and selection effects.

1. Separate the tests by physical sector

• Treat a merger as a joint test of generation, propagation and detection rather than as a single “test of general relativity”.
• Generation tests use inspiral, merger and post-merger gravitational-wave phasing, amplitudes, harmonics and polarisation content.
• Propagation tests compare gravitational-wave and electromagnetic arrival times, phases and distance-redshift relations.
• Matter-sector tests exploit tidal deformability, remnant fate, ejecta and kilonova or jet signatures, but require equation-of-state marginalisation.
• Equivalence-principle tests compare species-dependent propagation through intervening gravitational potentials.

2. Inspiral: strong-field generation constraints

• Parameterise departures in the frequency-domain phase while including general-relativistic tidal terms and calibration or waveform uncertainty.
• In scalar–tensor models, neutron stars can acquire scalar charges; scalar dipole radiation then produces a leading negative-post-Newtonian phasing contribution.
• Dynamical or spontaneous scalarisation can switch on nonperturbatively late in inspiral, motivating theory-specific numerical-relativity waveform families rather than only constant post-Newtonian deformation tests.
• Modified conservative dynamics can change binding energy, mass-radius relations and tidal Love numbers; the same measured phase may therefore admit gravity–equation-of-state degeneracies.
• Use binary-pulsar and Solar-System constraints as external priors only after checking their applicability to the chosen theory and screening regime.

3. Counterpart timing and propagation

• For GW170817, the observed gravitational-wave–gamma-ray-burst delay was +1.74 ± 0.05 seconds after a propagation distance of roughly 40 megaparsecs; subject to assumptions about intrinsic source delay, this tightly constrains differential gravitational-wave and photon propagation speed.
• Frequency-dependent gravitational-wave arrival phase tests modified dispersion, including massive-graviton-like terms, without requiring an electromagnetic trigger.
• Gravitational-wave and electromagnetic coincidence can test differential Shapiro delay and hence weak-equivalence-principle violation, but the inferred bound depends on the gravitational-potential model along the line of sight.
• A sequence of counterparts at differing redshifts can search for redshift- or environment-dependent propagation effects rather than relying on one nearby event.
• Neutrino counterparts would add a third messenger and potentially extend equivalence-principle and dispersion tests, but no binary-neutron-star neutrino counterpart presently provides such a constraint.

4. Amplitude, redshift and standard-siren tests

• The gravitational-wave waveform provides a gravitational-wave luminosity distance; host association from an electromagnetic counterpart supplies redshift and often better sky position.
• In many modified-gravity parameterisations, altered tensor friction or leakage gives a gravitational-wave luminosity distance different from the electromagnetic luminosity distance, even if tensor speed equals light speed.
• A joint hierarchical model should fit cosmology and modified propagation simultaneously; fixing a general-relativistic cosmology can falsely sharpen a gravity constraint.
• Afterglow imaging and modelling can constrain inclination, reducing the familiar distance–inclination degeneracy in the gravitational-wave amplitude.
• For high-redshift samples, include peculiar velocities, weak-lensing magnification, detector selection, host misidentification and counterpart detectability in the likelihood.

5. Matter-rich merger and post-merger observables

• Tidal deformabilities constrain the stellar response in the late inspiral, while post-merger spectral peaks and collapse time probe remnant structure at higher density.
• Kilonova colour, luminosity and spectra constrain ejecta mass, velocity, composition and possibly the remnant’s lifetime; these quantities depend jointly on the equation of state, binary parameters, neutrino and magnetohydrodynamic physics and gravity.
• A theory predicting altered stellar compactness, scalarisation or extra radiation can be challenged only by forward models that propagate its consequences through both gravitational-wave and electromagnetic observables.
• Use universal relations cautiously: relations calibrated in general relativity can become theory dependent and introduce hidden prior assumptions.
• The most defensible analysis jointly infers equation-of-state hyperparameters and gravity parameters across multiple mergers rather than treating an equation-of-state estimate as gravity independent.

6. Practical PhD-level inference strategy

• Define a theory-specific gravity parameter vector and explicit screening and stability priors; do not interpret generic post-Newtonian bounds as universal theory exclusions.
• Construct a joint likelihood for gravitational-wave, gamma-ray-burst, kilonova and afterglow data, retaining astrophysical nuisance parameters such as jet-launch delay and ejecta opacity.
• Compare general relativity and alternatives using evidences or predictive performance, while reporting posterior dependence on equation-of-state, population and counterpart-model assumptions.
• Combine events hierarchically, allowing source-dependent scalar charges and counterpart-selection functions instead of assuming all binary neutron-star events are identical.
• Validate claims with injection studies using alternative-theory signals, equation-of-state variation, realistic detector noise and deliberately mismatched electromagnetic models.

Evidence and debate

• Prompt gravitational-wave–gamma coincidence is the most direct multi-messenger constraint on anomalous tensor-wave speed.
  GW170817 and GRB 170817A were separated observationally by +1.74 ± 0.05 seconds. The collaboration reported a constraint on the fractional gravitational-wave–light speed difference of −3×10⁻¹⁵ to +7×10⁻¹⁶ under its timing interpretation.
  Limitation or counterpoint: The observed offset includes an unknown intrinsic delay between merger and gamma-ray production. A viable theory may also have luminal tensor speed while modifying generation, damping, polarisations or screening behaviour.
  Evidence strength: Very strong for the observed near-coincidence; model-dependent for conversion into a fundamental propagation-speed bound.
• The gravitational-wave signal supplies complementary tests of source dynamics and propagation even before electromagnetic information is used.
  The LIGO–Virgo GW170817 general-relativity test analysed dipole radiation, parameterised inspiral-phase deviations, modified dispersion, extra-dimensional leakage through gravitational-wave versus electromagnetic distance and polarisation content; its results were consistent with general relativity.
  Limitation or counterpoint: Generic deformation parameters do not uniquely correspond to a covariant alternative theory; tidal physics, waveform approximants and priors affect interpretation.
  Evidence strength: Strong as a broad, data-driven null test for the modelled deviations.
• Neutron-star mergers can probe nonperturbative strong-field gravity not fully tested by weak-field experiments.
  Numerical-relativity work in scalar–tensor gravity finds that binaries can differ markedly from general relativity in late inspiral and merger despite satisfying weak-field and binary-pulsar constraints, owing to spontaneous or dynamical scalarisation.
  Limitation or counterpoint: Scalarisation thresholds and predicted signals vary with coupling function, scalar mass, screening, stellar masses and equation of state; one cannot transfer a bound from one scalar–tensor realisation to all others.
  Evidence strength: Strong theoretical mechanism; observational reach is theory- and waveform-dependent.
• Electromagnetic redshifts turn binary neutron-star mergers into tests of modified gravitational-wave damping, friction and leakage, not merely Hubble-constant measurements.
  Modified-gravity propagation generically permits a gravitational-wave luminosity distance different from the electromagnetic luminosity distance; forecasts show that redshift-identified standard sirens can constrain phenomenological damping parameters.
  Limitation or counterpoint: The signal is entangled with cosmology, inclination, lensing, peculiar velocity, calibration, host identification and counterpart-selection effects. Current bright-siren statistics remain sparse.
  Evidence strength: Strong theoretical basis within the stated propagation parameterisations; future precision is forecast-dependent.
• Tidal, remnant and kilonova data offer additional gravity leverage only through a joint gravity–equation-of-state–astrophysics analysis.
  The GW170817 analysis explicitly required neutron-star tidal deformabilities in waveform models and emphasised that it was the first binary-neutron-star general-relativity test involving strong-field binary dynamics in the presence of matter.
  Limitation or counterpoint: Tidal and post-merger observables are sensitive to uncertain high-density matter and electromagnetic radiative-transfer and magnetohydrodynamic modelling; apparent deviations can be equation-of-state or astrophysical-model errors.
  Evidence strength: Strong methodological point.
• Multi-messenger timing can constrain non-universal propagation, but equivalence-principle bounds are less assumption-free than the observed coincidence itself.
  Studies of GW170817 have used multi-messenger timing to formulate weak-equivalence-principle tests via differential Shapiro delay, while stressing assumptions about the intervening potential.
  Limitation or counterpoint: Intrinsic emission delays and uncertain large-scale gravitational potentials limit how directly an arrival-time difference can be assigned to a violation of the equivalence principle.
  Evidence strength: Moderate: a highly sensitive timing lever arm, but interpretation rests on propagation and potential-modelling assumptions.

Uncertainties and research gaps

• The gamma-ray launch delay relative to merger is astrophysical and is not directly measured; it weakens any interpretation of gravitational-wave–gamma timing as a pure propagation-speed measurement.
• Dense-matter equation-of-state uncertainty can mimic or absorb modified-gravity effects in tidal phasing, remnant lifetime, ejecta mass and kilonova observables.
• Screening mechanisms and nonlinear strong-field phenomena mean that cosmological, Solar-System, binary-pulsar and neutron-star-merger constraints need not map onto a theory’s parameters in a model-independent way.
• Present direct multi-messenger leverage is dominated by GW170817; population-level claims will depend on the number, redshift distribution and counterpart-selection function of future events.
• Waveform-systematics control is incomplete for many alternative theories, especially through merger and post-merger, where fully relativistic matter simulations and detector-calibrated analyses are required.

Source suggestions

• Gravitational Waves and Gamma-rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A · LIGO scientific publication
• Tests of General Relativity with GW170817 · LIGO scientific publication
• Neutron-star mergers in scalar-tensor theories of gravity · Research paper
• The gravitational-wave luminosity distance in modified gravity theories · Research paper
• Tests of General Relativity with GW170817 — PDF · Scientific paper
• Multimessenger tests of the weak equivalence principle from GW170817 and its electromagnetic counterparts · Research paper