Spring 2012 Syllabus

Instructor: Roman Scoccimarro
Time: TR 9:30-10:45

• Special Relativity
  • Inertial Frames, Principle of Relativity, Lorentz Transformations, Michelson Morley Experiment
  • Spacetime, Coordinates and Invariance
  • Relativistic Kinematics and Dynamics
  • Variational Principle for Free Particle Motion, Light Rays
  
  
• Gravity as Geometry
  • Equivalence principle, Tests of Equality of Inertial and Gravitational Mass
  • Clocks in a Gravitational Field, Applications to the GPS
  • Local Inertial Frames, Light Cones, World Lines, Vectors
  • Geodesics, Symmetries and Conservation Laws
  
  
• Black Holes
  • Schwarszschild Geometry, Gravitational Redshift
  • Particle Orbits: Precession of the Perihelion of Mercury
  • Light Ray Orbits: Deflection and time Delay of Light (Gravitational Lensing)
  • Solar System Tests of General Relativity
  • Gravitational Collapse to a Black Hole
  • Astrophysical Back Holes (X-ray binaries, Galaxies, Hawking Radiation)
  
  
• Gravitational Waves
  • Linearized Gravitational Waves, Energy, Polarization
  • Detecting Gravitational Waves, Inteferometers
  
  
• Cosmology
  • Homogeneous and Isotropic Spacetimes: Expansion of the Universe, Cosmological Redshift
  • Matter, Radiation, Vacuum Energies: Evolution of FRW Models
  
  
• Einstein Equations
  • Tensors, Covariant Derivatives
  • Tidal Gravitational Forces, Riemann Curvature
  • Energy Momentum Conservation
  • Einstein Field Equations, Newtonian Limit
  • Applications: Production of Weak Gravitational Waves, Quadrupole Formula, Gravitational Radiation from Binary Pulsars