Contents › Part 5

Part 5 — General Relativity and Cosmology

1. The Equivalence Principle and Classical Tests
   • The universality of free fall
   • The equivalence principle in three strengths
   • Gravitational redshift
   • The perihelion of Mercury
   • The deflection of light
   • The Shapiro time delay
   • Relativity in the Global Positioning System
   • Beyond the classical tests
2. Geometric Formulation of Gravity
   • Geodesics as the trajectories of free fall
   • Curvature and tidal forces
   • The Einstein–Hilbert action
3. The Einstein Field Equations
   • The route to the field equations
   • The stress–energy tensor
   • The Bianchi identities
   • The Newtonian correspondence
   • The linearized theory
   • The cosmological constant
   • Lovelock's uniqueness theorem
   • Energy conditions
   • The initial-value problem
   • Exact solutions: an overview
4. Schwarzschild Geometry and Black Holes
   • The Schwarzschild solution
   • Geodesics and orbits
   • The horizon
   • Gravitational collapse
   • Rotating and charged black holes
   • Black-hole mechanics
   • The shadow
5. Gravitational-Wave Theory
   • Linearized gravity and the wave equation
   • Transverse-traceless gauge and the two polarizations
   • The quadrupole formula
   • Beyond linear order
6. Experiment: Gravitational Waves experiment
   • The Hulse–Taylor Binary Pulsar (PSR B1913+16) (1974–2016)
   • Direct detection: the instrument
   • GW150914 (2015)
   • The multimessenger outlook
7. Evidence-Based Cosmology
   • The expanding universe
   • The FLRW geometry
   • The thermal history
   • The cosmic microwave background
   • Large-scale structure
   • The accelerating universe
   • The $\Lambda$CDM parametrization
   • Inflation: the evidence status
8. Compact Stars and Relativistic Astrophysics
   • White dwarfs
   • Neutron stars
   • Pulsars
   • Maximum masses and radii
   • The black-hole endpoint
9. Experiment: Black-Hole Observations experiment
   • Historical context and the prediction under test
   • Apparatus
   • Procedure
   • Observations and data
   • Interpretation
   • Modern repetitions and precision
   • Primary references
10. Experiment: The Cosmic Microwave Background experiment
    • Historical context and the prediction under test
    • Apparatus
    • Procedure
    • Observations and data
    • Interpretation
    • Modern repetitions and precision
    • Primary references
11. Stellar Structure and Nucleosynthesis
    • The equations of stellar structure
    • Nuclear energy generation
    • The Hertzsprung–Russell diagram and stellar evolution
    • Stellar nucleosynthesis
    • Solar neutrinos
    • Helioseismology
12. Experiment: The Classical Tests of General Relativity experiment
    • Le Verrier and the perihelion of Mercury (1859)
    • Dyson, Eddington and Davidson: the eclipse of 1919
    • Pound, Rebka and Snider: redshift in a tower (1960–1965)
    • Shapiro: the radar time delay (1964–2003)
    • The Eötvös lineage and MICROSCOPE (1922–2022)
    • Lunar laser ranging and Gravity Probe B (1969–2011)
    • Summary of the evidence