Semester: 2016-2107 Fall

Contact Hours: 4 hours of lecture per week

The Spacetime of Special Relativity; Lorentz Transformations; Manifolds and Coordinates; Vector and Tensor Calculus on Manifolds; Electromagnetism; The Equivalence Principle and Spacetime Curvature; The Gravitational Field Equations; The Schwarzscild Geometry; Experimental Tests of General Relativity; Schwarzschild Black Holes; The Friedman-Robertson-Walker Geometry; Cosmological Models; Linearized General Relativity; Gravitational Waves.

Prerequisite(s): PHYS 212

Midterm2: %20 Second Midterm Exam 2016: pdf file (December 16)

Final: %30 Final Exam 2016: pdf file ((January 13, 9:00-11:00 SB-Z10)

Homework: %30

Minimum Requirements to Qualify for the Final Exam:

Midterms total must be > 50

1.

2.

3.

4.

Solutions of the First Homework Problems ,

5.

First Exercise set

Solutions of the Second Homework Problems ,

6.

Minkowski spacetime in Cartesian coordinates, Lorentz transformations, Cartesian basis vectors, Four-vectors and lightcone, Four vectors and Lorentz transformations, Four-velocity,Four-momentum of a massive particle, Four-momentum of a photon,Doppler effect and relativistic aberration, Relativistic mechanics, Free particles, Relativistic collisions and Compton scattering.

Solutions of the Third Homework Problems ,

Solutions of the First Midterm Exam Problems (2016) pdf file

7.

Newtonian gravity, The equivalence principle, Gravity as spacetime curvature, Local inertial coordinates, Weak gravitational fields and the Newtonian limit, intrinsic curvature of a manifold, The curvature tensor, Properties of Curvature tensor, The Ricci tensor and curvature scalar, Curvature and parallel transport, Curvature and Geodesic deviation.

Second Exercise set

8.

The energy momentum tensor,The energy momentum tesnor of a perfect fluid, Conservation of energy and momentum for a perfect fluid,The Einstein equations, The Einstein equations in empty space,The weak field limit of the Einstein equations, Geodesic motion from the Einstein equations (Reading assignment), Sign Conventions (Reading assignment).

9.

The general static isotropic metric, Solution of the empty-space field equations,Birkhoff's theorem, Gravitational redshift for a fixed emitter and receiver, Geodesics in the Schwarzschild geometry, Trajectories of massive particles,Radial motion of massive particles, Circular motion of massive particles,Stability of massive particle orbits, Trajectories of photons,Radial motion of photons, Circular motion of photons,Stability of photon orbits,

10.

Precession of planetary orbits, The bending of light,Gravitational Lensing,Radar echoes.

Solutions of the Second Midterm Exam Problems (2016) pdf file

11.

Solutions of the Final Exam Problems (2016) pdf file

12.The Friedman- Robertson-Walker Geometry

13.Cosmological Models

14.Linearized General Relativity

15.Gravitational Waves