Teaching

General relativity lectures:

Relativistic Elements:

• Euclid, Galileo, Newton, Kepler, Maxwell

•Lorentz and Poincaré

Relativistic Mechanics:

• Boost charge and the massless photon

• Relativistic mechanics, collisions, GZK, action, stress tensor

• Celerity, cone coordinates, proper(-ty) acceleration, and rapidity

Relativistic Electrodynamics:

• Coordinate-covariant electromagnetism

• Electromagnetic field as gauge curvature

Relativistic Geometry:

• Coordinate-covariant derivative operators & spacetime curvature 

• Bianchi, local conservation, curvature analog of homogeneous EM

Relativistic Fields:

• Generally covariant minimally coupled fields

• Maxwell and Dirac fields in curved spacetime

• Local Lorentz symmetry, tetrads, spin connection

• Energy of the gravitational field, Landau-Lifshitz pseudotensor. 

• Gravitational field in different dimensions

Relativistic Vacuum:

• Buchdahl limit, pressure gravitates, Schwarzschild spacetime 

• Weak tidal forces at the horizon of a supermassive black hole

• Interior volume of a Schwarzschild black hole

• White hole and parallel universes

• Singularity r=0 is not a point in space, and M is not located there

Relativistic Experiments:

•  Gravitational redshift

• Mercury's perihelion

• Shapiro time delay

• Deflection of light

• Orbiting gyroscopes

Classical mechanics lectures:

Elements:

• Bridgman’s and Buckingham Pi theorems

• Galilean group, Newtonian Perspective

• Strategies

Newton's Laws (inertial):

• Statics, Equal Forces, Torque Equilibrium 

• Using F=ma, Review of Dimensional Decomposition

• Gravity and electromagnetism force symmetry

Newton's Laws (non-inertial):

• Non-inertial frames, Coriolis, Euler, and Centrifugal

• Rotating Frame Effects on Earth: plumb lines and tower balls

• Foucault Pendulum and Larmor Precession

Oscillations (principles):

• Universality, Linearity, Decoupling

• Isochrony, Phase Space, Adiabatic Invariance

• Resonance as Poles, Stability and Symmetry Breaking, Spring Theory

• Oscillator Ladder, Oscillation Excitations, Occupation of a Single Oscillator

Oscillations (applications):

• Mechanical Electrical Oscillator

• Small Oscillations and Stability in 1D

• Many Degrees of Freedom, Matrix Method, Decoupling

• Small Oscillations of the Double Pendulum

• Normal Modes of the Linear Triatomic Molecule