GENERAL RELATIVITY
Class: Tuesdays and Thursdays, 9:30-10:45, Room 433 (Meyer Building)
Instructor: Roman Scoccimarro
Office Hours: Mondays 2-3PM, Room 506 Meyer. Or just email me.
Grades: Homework (60%), Final Exam (40%)
Recitations: Paul Duffell (pcd233 AT nyu.edu) [Mondays at 3:30pm in Room 333 Meyer]

### Final Exam

Will be on May 15, 8AM-9:50AM

### Textbook

• J.B. Hartle, Gravity, 2003, Addison Wesley

See also,

• B. Schutz, A First Course in General Relativity, 2nd edition, 2009, Cambridge Univeristy Press

### Homework [Due on Fridays, 3PM, Meyer 538]

• HMW1 [Feb 3]: Problems 2.4,3.2,4.2,4.7
• HMW2 [Feb 10]: Problems 4.13,4.18,5.2,5.4,5.9
• HMW3 [Feb 17]: Problems 6.3,6.8,6.11,6.13,6.14
• HMW4 [Feb 24]: Problems 7.5,7.10,7.14,7.22,7.23
• HMW5 [Mar 02]: Problems 8.3,8.5,8.9,8.11,9.1,9.2
• HMW6 [Mar 09]: Problems 9.5,9.6,9.9,9.10,9.18,9.21
• HMW7 [Mar 23]: Problems 10.4,12.3,12.4,12.5
• HMW8 [Mar 30]: Problems 12.8,12.11,12.14,16.6,16.7,16.8
• HMW9 [Apr 06]: Problems 18.3,18.4,18.5,18.16,18.19,18.28
• HMW10 [Apr 13]: Problems 20.4,20.7,20.13,20.17,20.18
• HMW11 [Apr 20]: Problems 21.6,21.7,21.13,21.14
• HMW12 [Apr 27]: Problems 22.5,22.8,22.9,22.13

### Lecture Notes

L1, L2, L3, L4, L5, L6, L7, L8, L9, L10, L11, L12, L13, L14, L15, L15.5, L16, L17, L17.5, L18, L19

Lecture Schedule (L# refers to notes above)

L1[Jan24-26] L2[Jan31] L3[Jan31-Feb2] L4[Feb7-9] L5[Feb9] L6[Feb14] L7[Feb16-21] L8[Feb21-23] L9[Feb28] L10[Mar01-06]
L11[Mar06-08] L12[Mar20-22] L13[Mar22-Mar27] L14[Mar29-Apr03] L15[Apr03-Apr05] L15.5[Apr05] L16[Apr10-12] L17[Apr17-19] L17.5[Apr19] L18[Apr24-26] L19[Apr26]

### Course Outline

• Special Relativity (2 weeks)
- 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 (2 weeks)
- 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 (3 weeks)
- 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 (1 week)
- Linearized Gravitational Waves, Energy, Polarization
- Detecting Gravitational Waves, Inteferometers

• Cosmology (2 weeks)
- Homogeneous and Isotropic Spacetimes: Expansion of the Universe, Cosmological Redshift
- Matter, Radiation, Vacuum Energies: Evolution of FRW Models

• Einstein Equations (3 weeks)
- 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