Relativity and Gravitation

Physics in 11 chapters — from “The postulates and the Lorentz transformation” to “Escape velocity, the Schwarzschild radius and the idea of a black hole”.

Chapters

  1. The postulates and the Lorentz transformation
    • Inertial frames and the Galilean transformation
    • The principle of relativity and light speed
    • Events and the light clock
    • The Lorentz transformation
    • Relativistic velocity addition
    • Problems
  2. Time dilation, length contraction and simultaneity
    • The muon and proper time
    • Length contraction and proper length
    • The relativity of simultaneity
    • The pole in the barn
    • The twin paradox
    • Problems
  3. Minkowski spacetime, four-vectors and causal structure
    • Spacetime diagrams and worldlines
    • The spacetime interval
    • Timelike, spacelike and lightlike separations
    • Causal structure and the order of events
    • Rapidity and the boost as rotation
    • Four-vectors and the four-velocity
    • The relativistic Doppler effect
    • Problems
  4. Relativistic momentum, energy and collisions
    • Relativistic momentum from a glancing collision
    • The four-momentum
    • The energy-momentum relation
    • Conservation of four-momentum
    • The invariant mass of a system
    • Threshold energy and two-body decays
    • Problems
  5. Mass as energy: binding, defect and annihilation
    • Rest energy and the atomic mass unit
    • Mass defect and binding energy
    • Mass-energy balance in reactions
    • Annihilation and pair production
    • Solar mass loss
    • Problems
  6. Gravitational field, potential and Gauss's law for gravity
    • Gravitational field strength and potential
    • Flux and Gauss's law for gravity
    • Shell theorem and the uniform sphere
    • Gravitational binding energy as a mass defect
    • Problems
  7. Tidal forces and the Newtonian tidal field
    • Relative acceleration of neighbouring free particles
    • Radial tidal acceleration
    • Transverse squeeze and the tidal field
    • Tracelessness of the tidal field in vacuum
    • Ocean tides
    • Roche limit and spaghettification
    • Problems
  8. Accelerated observers, hyperbolic motion and the equivalence principle
    • Proper acceleration and the accelerometer
    • Hyperbolic motion
    • The Rindler horizon
    • Clocks in an accelerating rocket
    • The equivalence principle
    • Light deflection in an accelerating laboratory
    • Problems
  9. Gravity as curved spacetime: redshift and local inertial frames
    • Gravitational redshift from the equivalence principle
    • Gravitational time dilation
    • Energy argument for the redshift
    • Local inertial frames and their size
    • Failure of flat-spacetime gravity
    • Curved spacetime and maximal proper time
    • Problems
  10. Experimental foundations: free fall, Lorentz invariance and clock tests
    • Universality of free fall and the Eötvös parameter
    • Torsion balances and the MICROSCOPE satellite
    • Local Lorentz invariance
    • Local position invariance and the tower test
    • Flying clocks and satellite navigation
    • The three pillars of the equivalence principle
    • Problems
  11. Escape velocity, the Schwarzschild radius and the idea of a black hole
    • Escape velocity and Michell's dark star
    • The compactness parameter
    • The event horizon
    • Tides at the horizon
    • Evidence for black holes
    • Problems