gravitational

Gravitational waves from nanohertz to terahertz, in one place: what they carry, how they travel, how sensitive every kind of detector is, and how far a detector can see. Strain conventions, noise curves, inspirals and binary pulsars, the black hole a merger leaves and how it rings, neutron-star tides, memory, the graviton's mass and number, stochastic backgrounds, high-frequency limits, lensing and cosmological distances, and the gravity of lab sources, each tested against published numbers. Pure Rust, SI units.

Install

cargo add gravitational metrology

Example: how far can Advanced LIGO see two neutron stars?

use gravitational::{curves, inspiral};
use metrology::{MPC, SOLAR_MASS};

let (m1, m2) = (1.4 * SOLAR_MASS, 1.4 * SOLAR_MASS);
let horizon = inspiral::horizon(m1, m2, 8.0, curves::aligo, 20.0);
let range = horizon / inspiral::HORIZON_TO_RANGE;
println!("horizon {:.0} Mpc, average range {:.0} Mpc", horizon / MPC, range / MPC);

Example: the strongest and the weakest

The brightest events radiate about a thousandth of the Planck luminosity c⁵/G; the oldest confirmed prediction is the slow decay of a binary pulsar's orbit. A detectable wave holds about 10³⁶ gravitons per wavelength-sized cell, yet matter is so transparent that water absorbs it over 10¹¹ Gpc.

use gravitational::{energy, propagation, quanta};
use metrology::{C, MPC, SOLAR_MASS};

assert!((3.5e49 / energy::PLANCK_LUMINOSITY - 9.6e-4).abs() < 1e-5); // GW150914 at its peak

let pbdot = energy::peters_pbdot(1.438 * SOLAR_MASS, 1.390 * SOLAR_MASS, 0.322997448918 * 86_400.0, 0.6171340);
println!("Hulse–Taylor: {pbdot:.3e} s/s"); // −2.402e-12; measured −2.40263(5)e-12

println!("{:.1e} gravitons", quanta::graviton_count(1e-21, 150.0)); // 3.9e36
let water = propagation::viscous_damping(1e-3, 1e3, 1e-12).unwrap();
println!("absorbed over {:.1e} Gpc of water", C / water / (1e3 * MPC)); // 2.6e11

Example: the ceiling on high-frequency waves

Any gravitational-wave background from the early Universe counts as extra radiation, so Big Bang nucleosynthesis and the CMB cap it. No detector built or proposed above 10 kHz reaches the cap.

use gravitational::{hf, strain::{Convention, hc_from_omega}};

let ceiling = hc_from_omega(hf::CEILING_BBN_CMB, 1e9, 1.0, Convention::OneSided);
println!("at 1 GHz no background can exceed h_c = {ceiling:.1e}"); // 1.3e-30

for limit in hf::REGISTRY {
    println!("{:<45} {:.1e} {} ({:?})", limit.name, limit.value, limit.quantity, limit.status);
}

Example: a gravity sensor as a wave detector

A wave of strain h stretches a baseline L, so two free masses feel a tidal acceleration ½ω²hL. Gradiometers, atom interferometers and satellite pairs all measure that; the baseline decides how well.

use gravitational::detectors::{AtomGwDetector, K_SR87, gradiometer_strain};

// AION-km: two strontium clouds 2 km apart (Badurina et al. 2020).
let aion = AtomGwDetector { baseline: 2000.0, t: 5.0, lmt: 40_000.0, phase_noise: 3e-6, k: K_SR87, diamonds: 1.0 };
println!("{:.1e} per √Hz at 0.1 Hz", aion.peak_strain()); // 2.1e-21

// A GOCE-class gradiometer (10 mE/√Hz) read the same way: 5e-11 per √Hz at 0.1 Hz.
assert!(gradiometer_strain(1e-11, 0.1) > 1e10 * aion.peak_strain());

What is inside

Applications

• Detector design. Horizon and range decide a detector's event rate, which is how next-generation designs are argued; examples/detector_range.rs works it through.
• Testing general relativity. examples/binary_pulsar.rs reproduces the Hulse–Taylor orbital decay from published orbital elements.
• Bounding a background. sgwb and hf convert between the strain, spectral density and energy-density conventions papers quote, and hf::REGISTRY carries the published limits with their status.
• Sizing a laboratory source. laboratory::quadrupole_strain says what a lab source radiates, and examples/lab_hfgw.rs sets it against the best detectors.
• Multi-messenger timing. propagation gives the speed bounds, dispersion and lensing delays.

How it is checked

Every formula is tested against numbers published in, or recomputed from, the papers above:

• Detectors: the LISA curve at five frequencies; the published peak strains of AION-10, AION-100, AION-km and AICE; Kolkowitz et al.'s clock strain.
• Binaries: the binary-neutron-star chirp mass, time to merger and ISCO; the decay of B1913+16 (to its quoted mass precision) and of the double pulsar; GW170817's spectral fluence; the double pulsar's periastron advance (to its 2PN term), Mercury's 42.98″ per century, S2's 12.1′ per orbit, the lunar de Sitter precession and Gravity Probe B's geodetic drift.
• Energy and quanta: the Planck luminosity; Blanchet's flux coefficients exactly; Tobar et al.'s rates and bar masses; Carney et al.'s occupation number; Aguiar's LSU bar cross-section.
• Propagation: GW170817's speed bounds; the graviton Compton wavelength against Bernus et al.; lensing magnifications and delays; viscous damping in water and air, and its refusal for a mantle.
• Backgrounds: NANOGrav's energy density; Hellings–Downs values; inflation's energy scale for r = 0.036, 0.034 and 0.01.
• The lab: the petawatt beam; the Misner–Thorne–Wheeler spinning rod; LIGO's rotor force (19.10 pN by direct summation) and Virgo's x f² = 3.3×10⁻¹⁴ m Hz²; Ejlli et al.'s photon-rate prefactor; an ADMX-like cavity.

All formulas are written from the papers, not translated from other codes, so the crate stays MIT-licensed. The research behind the newer modules is in the report on where gravity physics is still open.

One of eight crates in physica: physica (all of them, plus cross-domain analogies) · metrology (constants) · geopotential (the gravity field) · gravimetry (missions and GRACE) · gravitational (waves) · gravitics (frontier gravity) · magnetics (magnetism and MHD) · plasmoid (fusion plasma).