Фізика гравітаційних хвиль

🌊 Гравітаційні хвилі

Теорія Einstein

General relativity: h_μν metric perturbations. Transverse-traceless gauge: 2 polarization states (+, ×). Wave equation: □h_μν = 0.

Generation

Quadrupole moment: Q̈_ij ~ h. Binary systems: периодичні зміни Q. Power: P ~ (d³Q/dt³)².

Propagation

Speed: c (швидкість світла). Amplitude: h ~ 1/r. BBN/CMB limits: ~10⁻³⁰ strains на early Universe.

Effects

Просторове спотворення: ΔL/L ~ h. Doppler effect на test masses. Quadrupolar pattern.

🔬 LIGO/Virgo

Interferometer

Michelson: 4 km arms, 90° separation. Laser beams з mirrors. Path difference: ΔL ~ h·L для strain h.

Sensitivity

Advanced LIGO: h ~ 10⁻²¹. Frequency range: 10-1000 Hz. Quantum noise, seismic, thermal limits. Third-generation: 10⁻²²-10⁻²³.

Detection

Matched filtering: template waveforms vs data. Signal-to-noise ratio SNR ≥ 5. Coincidence LIGO Livingston, Hanford, Virgo.

Network

LIGO, Virgo, KAGRA (Японія). Future LIGO-India. Localization: triangulation. Sky localization ~20 deg² для 3 detectors.

⚫ Black hole mergers

GW150914

First detection (2015): 30+20 M☉, z ~ 0.1. M_chirp ≈ 28 M☉. Total energy ~3 M☉c². Duration ~0.2 s.

Inspiral

Binary orbit decay: energy loss through GWs. Frequency chirp: f(t) зростає. Post-Newtonian expansion.

Merger

Relativistic plunge: last orbits. Numerical Relativity simulations. Quasinormal modes: ringdown.

Population

~100+ events: 10-100 M☉ black holes. Primordial vs stellar-origin. Binary formation channels.

⭐ Neutron star mergers

GW170817

NS-NS merger (2017): 1.4+1.3 M☉. Electromagnetic counterpart: GRB 170817A, kilonova. Multimessenger astronomy.

Kilonova

r-process nucleosynthesis: heavy elements (Au, Pt). Blue to red kilonova. Emission time ~days.

Tidal effects

Deformability: tidal Love numbers. Equation of state constraints. NS radius ~10-15 km.

EM counterparts

Short GRBs, kilonova, afterglow. Coordinates, distance, NS physics. r-process elements origin.

🌊 Waveform modeling

Post-Newtonian

v/c expansion: 5.5PN order. Analytic for inspiral. Chirp: f(t) ~ (T-t)^(-3/8). Orbital evolution.

Effective One-Body

EOB: mapping to one-body problem. Resummation, calibration to NR. Inspiral → merger → ringdown.

Numerical Relativity

Simulations: Einstein equations. Black hole mergers, NS mergers. Waveform banks, parameter space.

Template banks

Matched filtering: waveform libraries. Masses, spins, eccentricity coverage. PyCBC, LALSuite.

🔬 Applications

Black hole physics

No-hair theorem tests. Quasinormal modes. Stability, horizons. Kerr metric validation.

Neutron star equation of state

Tidal deformability Λ. Radius constraints. Nuclear physics, QCD. EoS reconstruction.

Cosmology

Standard sirens: distance-redshift. H₀ ~ 70 км/(с·Mpc) з GW170817. Future: redshifts z > 1.

Tests gravity

Dipole radiation, extra dimensions. Modified gravity constraints. Propagation speed: |c_g/c - 1| < 10⁻¹⁵.

📊 Графіки та діаграми

Binary merger phases

Waveform evolution:

Energy spectrum: ~milliseconds для merger. LIGO band: 10-1000 Hz.

LIGO sensitivity

Strain noise:

Optimal sensitivity: ~100 Hz. Third-generation: 10⁻²³ strains.

Inspiral: h(t) ∝ f^(2/3)·e^(-iΦ(t)) Chirp: f(t) ~ (T-t)^(-3/8) Merger: peak amplitude Ringdown: h(t) ∝ e^(-t/τ)·sin(ωt) Duration ~0.1-1 s

🧪 Практичні приклади

Приклад 1: GW150914

Black holes 30+20 M☉, z ~ 0.1. M_chirp ≈ 28 M☉. Duration ~0.2 s. SNR ~24. LIGO Hanford + Livingston.

Приклад 2: GW170817

NS-NS merger: 1.4+1.3 M☉. GRB 170817A (1.7 s delay). Kilonova (blue → red). ~100 EM telescopes.

Приклад 3: GW190521

~85+66 M☉ → 142 M☉ remnant. Intermediate-mass BH. GW alone (no EM). z ~ 0.8.

Приклад 4: LISA mission

Space-based: 2.5 Mkm arms. Low frequencies 0.1-100 mHz. Supermassive BH mergers, EMRIs.

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Гравітаційні хвилі: хвилі простору-часу

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