General Relativity

7.

Gravitational Waves

7.1.

Theoretical Foundation

7.1.1.

The Nature of Gravitational Waves

7.1.1.1.

Ripples in Spacetime

7.1.1.2.

Transverse Nature

7.1.1.3.

Speed of Propagation

7.1.2.

Linearized Einstein Equations

7.1.2.1.

Weak-Field Approximation

7.1.2.2.

7.1.2.3.

Gauge Conditions

7.1.3.

Polarization of Gravitational Waves

7.1.3.1.

Plus Polarization

7.1.3.2.

Cross Polarization

7.1.3.3.

7.1.4.

Energy and Momentum Transport

7.1.4.1.

Stress-Energy Pseudotensor

7.1.4.2.

7.1.4.3.

Momentum Density

7.2.

Generation of Gravitational Waves

7.2.1.

Quadrupole Formula

7.2.1.1.

Quadrupole Moment

7.2.1.2.

Time-Varying Mass Distribution

7.2.1.3.

7.2.2.

Sources of Gravitational Waves

7.2.2.1.

7.2.2.1.1.

7.2.2.1.2.

7.2.2.1.3.

7.2.2.2.

Coalescing Compact Objects

7.2.2.2.1.

Neutron Star Mergers

7.2.2.2.2.

Black Hole Mergers

7.2.2.2.3.

Merger and Ringdown Phases

7.2.2.3.

7.2.2.3.1.

7.2.2.3.2.

Asymmetric Explosions

7.2.2.4.

Rotating Neutron Stars

7.2.2.4.1.

Pulsar Glitches

7.2.2.4.2.

Mountains on Neutron Stars

7.2.2.5.

Stochastic Background

7.2.2.5.1.

Primordial Gravitational Waves

7.2.2.5.2.

Cosmological Sources

7.3.

Detection Methods

7.3.1.

Laser Interferometry

7.3.1.1.

Michelson Interferometer Principle

7.3.1.2.

Strain Sensitivity

7.3.1.3.

7.3.1.3.1.

7.3.1.3.2.

7.3.1.3.3.

7.3.1.3.4.

7.3.2.

Ground-Based Detectors

7.3.2.1.

7.3.2.1.1.

7.3.2.1.2.

Sensitivity Curve

7.3.2.2.

7.3.2.2.1.

European Detector

7.3.2.2.2.

Collaboration with LIGO

7.3.2.3.

7.3.2.3.1.

Japanese Detector

7.3.2.3.2.

Underground Location

7.3.2.4.

Future Detectors

7.3.2.4.1.

Einstein Telescope

7.3.2.4.2.

Cosmic Explorer

7.3.3.

Space-Based Detection

7.3.3.1.

7.3.3.1.1.

Laser Interferometer Space Antenna

7.3.3.1.2.

Millihertz Frequency Band

7.3.3.1.3.

Constellation Design

7.3.3.2.

Other Proposed Missions

7.3.4.

Pulsar Timing Arrays

7.3.4.1.

Millisecond Pulsars as Clocks

7.3.4.2.

Nanohertz Gravitational Waves

7.3.4.3.

Supermassive Black Hole Binaries

7.3.5.

7.3.5.1.

Matched Filtering

7.3.5.2.

7.3.5.3.

Parameter Estimation

7.3.5.4.

Signal Extraction Techniques

7.4.

Observational Results

7.4.1.

First Detection: GW150914

7.4.1.1.

Binary Black Hole Merger

7.4.1.2.

Confirmation of Einstein's Prediction

7.4.2.

Multi-messenger Astronomy

7.4.2.1.

GW170817: Neutron Star Merger

7.4.2.2.

Electromagnetic Counterparts

7.4.2.3.

Gamma-Ray Bursts

7.4.3.

Population Studies

7.4.3.1.

Black Hole Mass Distribution

7.4.3.2.

7.4.3.3.

Cosmological Implications

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